B.COM SEM 3 Statistical Methods

(BASIC MCQ)

UNIVERSITY OF LUCKNOW

(VERY IMPORTANT MCQ FOR STATICAL METHOD)

MCQs

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Unit 1:Introduction

The Nature and scope of statistics, Definition of statistics. Law of Statistical Regularity: Law of Inertia of Large Numbers. Census and Sampling, Methods of Sampling, Types and Characteristics of Statistical Unit. Methods and instruments of data collection.

MCQs

1] statistics deals with
a] qualitative analysis b] numerical facts
c] immaterial analysis

2] statistical methods are used by
a] govt. b] firms
c]researcher d] all of above

1. A numerical value used as a summary measure for a sample, such as a sample mean, is known as a

A) Population Parameter

B) Sample Parameter

C) Sample Statistic

D) Population Mean

Answer: C

2. Statistics branches include

A) Applied Statistics

B) Mathematical Statistics

C) Industry Statistics

D) Both A and B

Answer: D

3. To enhance a procedure the control charts and procedures of descriptive statistics are classified into

A) Behavioural Tools

B) Serial Tools

C) Industry Statistics

D) Statistical Tools

Answer: A

4. Sample statistics are also represented as

A) Lower Case Greek Letter

B) Roman Letters

C) Associated Roman Alphabets

D) Upper Case Greek Letter

Answer: B

5. Individual respondents, focus groups, and panels of respondents are categorised as

A) Primary Data Sources

B) Secondary Data Sources

C) Itemised Data Sources

D) Pointed Data Sources

Answer: A

6. The variables whose calculation is done according to the weight, height and length and weight are known as:

A) Flowchart Variables

B) Discrete Variables

C) Continuous Variables

D) Measuring Variables

Answer: C

7. A method used to examine inflation rate anticipation, unemployment rate and capacity utilisation to produce products is classified as

A) Data Exporting Technique

B) Data Importing Technique

C) Forecasting Technique

D) Data Supplying Technique

Answer: C

8. Graphical and numerical methods are specialized processes utilised in

A) Education Statistics

B) Descriptive Statistics

C) Business Statistics

D) Social Statistics

Answer: B

9. The scale applied in statistics which imparts a difference of magnitude and proportions is considered as

A) Exponential Scale

B) Goodness Scale

C) Ratio Scale

D) Satisfactory Scale

Answer: C

10. Review of performance appraisal, labour turnover rates, planning of incentives and training programs and are examples of

A) Statistics in Production

B) Statistics in Marketing

C) Statistics in Finance

D) Statistics in Personnel Management

Answer: D

1.The building blocks of a theory is called

A. Definitions

B. Concepts

C. Propositions

D. Variables

2.“Statistics are effected to a marked extend by .....................”

a) Aggregate of facts

b) multiplicity of causes

c) numerically stated

d) complex manifestations

3.The Mathematical theory of probability has helped to form the ..............

a) Statistical theory

b) Law of Inertia of large numbers

c) Law of statistical Relativity

d) Law of statistical Regularity

4.Which among the following is not a merit of the census method?

a) Results are representative

b) Information on rare events

c) Results are reliable

d) In appropriate method for enumeration

5.The basic objective of sampling study is ........................

a) to draw inference

b) to check units of population

c) to collect numerical data

d) to make census

6. ________ implies a smaller representation of a larger whole.

a) Survey

b) Population

c) Sample

d) Census

7.The prominent meaning of ‘statistics’...............

a) Data, its analysis and interpretation

b) observation of samples

c) Method for analysingnumers

d) conducting census

8.(i) the results derived from sampling method may be different from population

(ii) Sampling method derives only the same characteristics of the population Choose the correct from the following:

a) Both the statements are correct

b) Both the statements are wrong

c) Only the first statement is correct

d) only the second statement is correct

9.Which among the following is not an essential of sampling?

a) Representativeness

b) Complete

c) Same

d) Dependent

10.“More reliable results can be obtained through sampling method”, because ……........

a) Statistical error is low

b) Saves time

c) Cost is low

d) None of the above

11.Non-proportional random sampling is a sub-type of....................

a) Unrestricted random sampling

b) Simple Random Sampling

c) Stratified Random Sampling

d) Cluster Random Sampling

12 A ________ refers to any collection of specified group of human beings

a) Sampling

b) Population

c) Random sampling

d) Non probability sampling

13.It is the collection of data concerning the living and working conditionals of the people in a given community.

a) Sampling

b) Social survey

c) Case study

d) Data collection

14. _________ are the most complete type of survey.

a) Social survey

b) Sampling

c) Censuses

d) Data collection

15."The process of selecting the sample from the population" is called

a)scale

b)standard error

c)statistics

d)sampling

16.The list of all units in a population is called

a) Random sampling

b) Sampling Frame

c) Bias

d) Parameter

e) Statistic

Methods of Data Collection

1.Questionnaire is a

a. Research method

b. Measurement technique

c. Tool for data collection

d. Data analysis technique

Answer: c

2.What does the term 'reliability' indicate?

a.We can trust that the research has being carried out to a high standard.

b.That the results are accurate.

c.That the researcher can be trusted.

d.That the tool of data collection can be regarded as measuring accurately and consistently.

Answer: d

5. What is the problem(s) with this set of response categories to the question “What is your current age?”

1-5

5-10

10-20

20-30

30-40

a. The categories are not mutually exclusive

b. The categories are not exhaustive

c. Both a and b are problems

d. There is no problem with the above set of response categories

Answer: c

6.Questionnaires can address events and characteristics taking place when?

a. In the past (retrospective questions)

b. In the present (current time questions)

c. In the future (prospective questions)

d. All of the above

Answer: d

7. Which of the following are principles of questionnaire construction?

a. Consider using multiple methods when measuring abstract constructs

b. Use multiple items to measure abstract constructs

c. Avoid double-barrelled questions

d. All of the above

Answer: d

8. Which of these is not a method of data collection.

a. Questionnaires

b. Interviews

c. Experiments

d. Observations

Answer: c

9. Secondary/existing data may include which of the following?

a. Official documents

b. Personal documents

c. Archived research data

d. All of the above

Answer: d

10. Which of the following terms best describes data that were originally collected at an earlier time by a different person for a different purpose?

a. Primary data

b. Secondary data

c. Experimental data

d. Field notes

Answer: b

12. Open-ended questions provide primarily data.

a. Confirmatory data

b. Qualitative data

c. Predictive data

d. None of the above

Answer: b

13. Which of the following is true concerning observation?

a. It takes less time

b. It costs less money

c. It is often not possible to determine exactly why the people behave as they do

d. All of the above

Answer: c

14. When constructing a questionnaire it is important to do each of the following except .

a. Use "leading" or "loaded" questions

b. Use natural language

c. Understand your research participants

d. Pilot your test questionnaire

Answer: a

16. The type of interview in which the specific topics are decided in advance but the sequence and wording can be modified during the interview is called:

a. The interview guide approach

b. The informal conversational interview

c. A closed quantitative interview

d. The standardised open-ended interview

Answer: a

17. Which one of the following in not a major method of data collection:

a. Questionnaires

b. Interviews

c. Secondary data

d. All of the above are methods of data collection

Answer: d

18. A question during an interview such as “Why do you feel that way?” is known as a

a. Probe

b. Filter question

c. Response

d. Pilot

Answer: a

19. A census taker often collects data through which of the following?

a. Standardised tests

b. Interviews

c. Secondary data

d. Observations

Answer: b

20. The researcher has secretly placed him or herself (as a member) in the group that is being studied. This researcher may be which of the following?

a. A complete participant

b. An observer-as-participant

c. A participant-as-observer

d. None of the above

Answer: a

21. Which of the following is not a major method of data collection?

a. Questionnaires

b. Focus groups

c. Correlational method

d. Secondary data

Answer: c

22. Which type of interview allows the questions to emerge from the immediate context or course of things?

a. Interview guide approach

b. Informal conversational interview

c. Closed quantitative interview

d. Standardised open-ended interview

Answer: b

25. An ordinal scale is used to rank order people, objects, or characteristics.

a. True

b. False

Answer: a

26. Which scale is the simplest form of measurement?

a. Nominal

b. Ordinal

c. Interval

d. Ratio

Answer: a

27. tests focus on information acquired through the informal learning that goes on in life.

a. Personality

b. Achievement

c. Aptitude

d. Intelligence

Answer: c

28. If a cricket coach calculates batting averages, what scale would be used?

a. Interval scale

b. Ratio scale

c. Nominal scale

d. Ordinal scale

Answer: b

29. An ordinal scale is:

a. The simplest form of measurement

b. A rank-order scale of measurement

c. A scale with equal intervals between adjacent numbers

d. A scale with an absolute zero point

Answer: b

30. Qualitative observation is usually done for exploratory purposes; it is also called observation.

a. Structured

b. Naturalistic

c. Complete

d. Probed

Answer: b

Unit –II Classification and Tabulation

Objects, general rules for the construction of tables. Measures of Central Tendency: Mean – Simple and Weighted, Mode, Harmonic and Geometric Mean; Positional Averages- Median, Quartile and Percentiles.

1] which one is not a statistical methods
a] classification b] tabulation
c] analysis d] numerical data

2] regression is used for
a] collection of data b] organisation of data
c] classification d] analysis

3] which one is not an economic problem
a] what is produce b] how to produce
c] where to produce d] how to pronounce

Question 1:The arrangement of data in rows and columns is called

(A) Frequency distribution

(B) Cumulative frequency distribution

(D) Classification

Answer C

Question 2:When the quantitative and qualitative data are arranged according to a single feature, the tabulation is known as

(A) One-way

(B) Bivariate

(D) Dichotomy

Answer A

Question 3:Which function does the tabulation origin spot specify?

(A) The list of integers

(B) The list of max terms

(D) None

Answer A

Question 4:In the table, the unchecked term is known as

(A) Prime Implications

(B) Old Implications

(D) None

Answer A

Question 5:Tabulation form exercises

(A) Gates

(B) Demorgan’s postulate

(D) Venn diagram

Answer C

Question 6:The first tabulation method was known as

(A) Quine-McCluskey

(B) Cluskey

(D) None

Answer D

Question 7:The table where the variables are subdivided with interrelated features are known as

(A) Order level table

(B) Sub parts of table

(D) Two-way table

Answer D

Question 8:In a tabular presentation, the summary and presentation of data with different non-overlapping classes are defined as

(A) Frequency distribution

(B) Chronological distribution

(D) Nominal distribution

Answer A

Question 9:General tables of data used to show data in an orderly manner are called as

(A) Double characteristic table

(B) Manifold tables

(D) Single characteristics tables

Answer C

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MCQ’S OF MEASURES OF CENTRAL TENDENCY

MCQ No 3.1

Any measure indicating the centre of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of:

(a) Skewness (b) Symmetry (c) Central tendency (d) Dispersion

MCQ No 3.2

Scores that differ greatly from the measures of central tendency are called:

(a) Raw scores (b) The best scores (c) Extreme scores (d) Z-scores

MCQ No 3.3

The measure of central tendency listed below is:

(a) The raw score (b) The mean (c) The range (d) Standard deviation

MCQ No 3.4

The total of all the observations divided by the number of observations is called:

(a) Arithmetic mean (b) Geometric mean (c) Median (d) Harmonic mean

MCQ No 3.5

While computing the arithmetic mean of a frequency distribution, the each value of a class is considered equal to:

(a) Class mark (b) Lower limit (c) Upper limit (d) Lower class boundary

MCQ No 3.6

Change of origin and scale is used for calculation of the:

(a) Arithmetic mean (b) Geometric mean

MCQ No 3.7

The sample mean is a:

(a) Parameter (b) Statistic (c) Variable (d) Constant

MCQ No 3.8

The population mean µ is called:

(a) Discrete variable (b) Continuous variable (c) Parameter (d) Sampling unit

MCQ No 3.9

The arithmetic mean is highly affected by:

(a) Moderate values (b) Extremely small values

MCQ No 3.10

The sample mean is calculated by the formula:

If a constant value is added to every observation of data, then arithmetic mean is obtained by:

(a) Subtracting the constant (b) Adding the constant

MCQ No 3.12

Which of the following statements is always true?

(a) The mean has an effect on extreme scores (b) The median has an effect on extreme scores

MCQ No 3.13

The elimination of extreme scores at the bottom of the set has the effect of:

(a) Lowering the mean (b) Raising the mean (c) No effect (d) None of the above

MCQ No 3.14

The elimination of extreme scores at the top of the set has the effect of:

(a) Lowering the mean (b) Raising the mean (c) No effect (d) Difficult to tell

MCQ No 3.15

The sum of deviations taken from mean is:

(a) Always equal to zero (b) Some times equal to zero

MCQ No 3.16

If = 25, which of the following will be minimum:

(a) ∑(X – 27)² (b) ∑(X – 25)² (c) ∑(X – 22)² (d) ∑(X + 25)²

MCQ No 3.17

The sum of the squares fo the deviations about mean is:

(a) Zero (b) Maximum (c) Minimum (d) All of the above

MCQ No 3.18

(a) 10 (b) 50 (c) 60 (d) 100

MCQ No 3.19

For a certain distribution, if ∑(X -20) = 25, ∑(X- 25) =0, and ∑(X-35) = -25, then is equal to:

(a) 20 (b) 25 (c) -25 (d) 35

MCQ No 3.20

The sum of the squares of the deviations of the values of a variable is least when the deviations are measured from:

(a) Harmonic mean (b) Geometric mean (c) Median (d) Arithmetic mean

MCQ No 3.21

If X₁, X₂, X₃, ... X_n, be n observations having arithmetic mean and if Y =4X ± 2, then is equal to:

(a) 4X (b) 4 (c) 4 ± 2 (d) 4 ± 2

If =100 and Y=2X – 200, then mean of Y values will be:

(a) 0 (b) 2 (c) 100 (d) 200

MCQ No 3.23

Step deviation method or coding method is used for computation of the:

(a) Arithmetic mean (b) Geometric mean (c) Weighted mean (d) Harmonic mean

MCQ No 3.24

If the arithmetic mean of 20 values is 10, then sum of these 20 values is: (a) 10 (b) 20 (c) 200 (d) 20 + 10

MCQ No 3.25

Ten families have an average of 2 boys. How many boys do they have together? (a) 2 (b) 10 (c) 12 (d) 20

MCQ No 3.26

If the arithmetic mean of the two numbers X₁ and X₂ is 5 if X₁=3, then X₂ is: (a) 3 (b) 5 (c) 7 (d) 10

MCQ No 3.27

Given X₁=20 and X₂= -20. The arithmetic mean will be:

(a) Zero (b) Infinity (c) Impossible (d) Difficult to tell

MCQ No 3.28

The mean of 10 observations is 10. All the observations are increased by 10%. The mean of increased observations will be:

(a) 10 (b) 1.1 (c) 10.1 (d) 11

MCQ No 3.29

The frequency distribution of the hourly wage rate of 60 employees of a paper mill is as follows:

Wage rate (Rs.)	54----56	56----58	58----60	60----62	62----64
Number of workers	10	10	20	10	10

The mean wage rate is:

(a) Rs. 58.60 (b) Rs. 59.00 (c) Rs. 57.60 (d) Rs. 57.10

MCQ No 3.30

The sample mean of first n natural numbers is:

(a) n(n+ 1) / 2 (b) (n+ 1) / 2 (c) n/2 (d) (n+ 1) / 2

MCQ No 3.31

The mean of first 2n natural numbers is:

MCQ No 3.32

The sum of deviations is zero when deviations are taken from:

(a) Mean (b) Median (c) Mode (d) Geometric mean

When the values in a series are not of equal importance, we calculate the:

(a) Arithmetic mean (b) Geometric mean (c) Weighted mean (d) Mode

MCQ No 3.34

When all the values in a series occur the equal number of times, then it is not possible to calculate the:

(a) Arithmetic mean (b) Geometric mean (c) Harmonic mean (d) Weighted mean

MCQ No 3.35

The mean for a set of data obtained by assigning each data value a weight that reflects its relative importance within the set, is called:

(a) Geometric mean (b) Harmonic mean (c) Weighted mean (d) Combined mean

MCQ No 3.36

If 1, 2, 3, ... , k be the arithmetic means of k distributions with respective frequencies n₁, n₂, n3, ... , n_k, then the mean of the whole distribution c is given by:

(a) ∑ / ∑n (b) ∑n / ∑ (c) ∑n / ∑n (d) ∑(n+ ) / ∑n

MCQ No 3.37

The combined arithmetic mean is calculated by the formula:

MCQ No 3.38

The arithmetic mean of 10 items is 4 and the arithmetic mean of 5 items is 10. The combined arithmetic mean is:

(a) 4 (b) 5 (c) 6 (d) 90

MCQ No 3.39

The midpoint of the values after they have been ordered from the smallest to the largest or the largest to the smallest is called:

(a) Mean (b) Median (c) Lower quartile (d) Upper quartile

MCQ No 3.40

The first step in calculating the median of a discrete variable is to determine the:

(a) Cumulative frequencies (b) Relative weights

MCQ No 3.41

The suitable average for qualitative data is:

(a) Mean (b) Median (c) Mode (d) Geometric mean

MCQ No 3.42

Extreme scores will have the following effect on the median of an examination:

(a) They may have no effect on it (b) They may tend to raise it

MCQ No 3.43

We must arrange the data before calculating:

(a) Mean (b) Median (c) Mode (d) Geometric mean

If the smallest observation in a data is decreased, the average which is not affected is:

(a) Mode (b) Median (c) Mean (d) Harmonic mean

MCQ No 3.45

If the data contains an extreme value, the suitable average is:

(a) Mean (b) Median (c) Weighted mean (d) Geometric mean

MCQ No 3.46

Sum of absolute deviations of the values is least when deviations are taken from:

(a) Mean (b) Mode (c) Median (d) Q₃

MCQ No 3.47

The frequency distribution of the hourly wages rate of 100 employees of a paper mill is as follows:

Wage rate (Rs.)	54----56	56----58	58----60	60----62	62----64
Number of workers	20	20	20	20	20

The median wage rate is:

(a) Rs.55 (b) Rs.57 (c) Rs.56 (d) Rs.59

MCQ No 3.48

The values of the variate that divide a set of data into four equal parts after arranging the observations in ascending order of magnitude are called:

(a) Quartiles (b) Deciles (c) Percentiles (d) Difficult to tell

MCQ No 3.49

The lower and upper quartiles of a symmetrical distribution are 40 and 60 respectively. The value of median is:

(a) 40 (b) 50 (c) 60 (d) (60 – 40) / 2

MCQ No 3.50

If in a discrete series 75% values are less than 30, then:

(a) Q₃ < 75 (b) Q₃ < 30 (c) Q₃ = 30 (d) Q₃ > 30

MCQ No 3.51

If in a discrete series 75% values are greater than 50, then:

(a) Q₁ = 50 (b) Q₁ < 50 (c) Q₁ > 50 (d) Q₁ ≠ 50

MCQ No 3.52

If in a discrete series 25% values are greater than 75, then:

(a) Q₁ > 75 (b) Q₁ = 75 (c) Q₃ = 75 (d) Q₃ > 75

MCQ No 3.53

If in a discrete series 40% values are less than 40, then :

(a) D₄ ≠ 40 (b) D₄ < 40 (c) D₄ > 40 (d) D₄ = 40

MCQ No 3.54

If in a discrete series 15% values are greater than 40, then:

(a) P₁₅ = 70 (b) P₈₅ = 15 (c) P₈₅ = 70 (d) P₇₀ = 70

MCQ No 3.55

The middle value of an ordered series is called:

(a) Median (b) 5^th decile (c) 50^th percentile (d) All the above

If in a discrete series 50% values are less than 50, then:

(a) Q₂ = 50 (b) D₅ = 50 (c) P₅₀ = 50 (d) All of the above

MCQ No 3.57

The mode or model value of the distribution is that value of the variate for which frequency is:

(a) Minimum (b) Maximum (c) Odd number (d) Even number

MCQ No 3.58

Suitable average for averaging the shoe sizes for children is:

(a) Mean (b) Mode (c) Median (d) Geometric mean

MCQ No 3.59

Extreme scores on an examination have the following effect on the mode:

(a) They tend to raise it (b) they tend to lower it

MCQ No 3.60

A measurement that corresponds to largest frequency in a set of data is called:

(a) Mean (b) Median (c) Mode (d) Percentile

MCQ No 3.61

Which of the following average cannot be calculated for the observations 2, 2, 4, 4, 6, 6, 8, 8, 10, 10 ?

(a) Mean (b) Median (c) Mode (d) All of the above

MCQ No 3.62

Mode of the series 0, 0, 0, 2, 2, 3, 3, 8, 10 is:

(a) 0 (b) 2 (c) 3 (d) No mode

MCQ No 3.63

A distribution with two modes is called:

(a) Unimodel (b) Bimodal (c) Multimodal (d) Normal

MCQ No 3.64

The model letter of the word “STATISTICS” is:

(a) S (b) T (c) Both S and I (d) Both S and T

MCQ No 3.65

The mode for the following frequency distribution is:

Weekly sales of burner units	0	1	2	3	Over 3
Number of weeks	38	6	5	1	0

(a) 0 (b) 2 (c) 3 (d) No mode

MCQ No 3.66

Which of the following statements is always correct?

(a) Mean = Median = Mode (b) Arithmetic mean = Geometric mean = Harmonic mean

MCQ No 3.67

In a moderately symmetrical series, the arithmetic mean, median and mode are related as:

(a) Mean - Mode = 3(Mean - Median) (b) Mean - Median = 2(Median - Mode)

In a moderately skewed distribution, mean is equal to!

(a) (3Median - Mode) / 2 (b) (2Mean + Mode) / 3

MCQ No 3.69

In a moderately asymmetrical distribution, the value of median is given by:

(a) 3Median + 2Mean (b) 2Mean + Mode

MCQ No 3.70

For moderately skewed distribution, the value of mode is calculated as:

(a) 2Mean – 3Median (b) 3Median – 2Mean

MCQ No 3.71

In a moderately skewed distribution, Mean = 45 and Median = 30, then the value of mode is:

(a) 0 (b) 30 (c) 45 (d) 180

MCQ No 3.72

If for any frequency distribution, the median is 10 and the mode is 30, then approximate value of mean is equal to:

(a) 0 (b) 10 (c) 30 (d) 60

MCQ No 3.73

In a moderately asymmetrical distribution, the value of mean and mode is 15 and 18 respectively. The value of median will be:

(a) 48 (b) 18 (c) 16 (d) 15

MCQ No 3.74

(a) 2 (b) 3 (c) 1/2 (d) 1/3

MCQ No 3.75

Which of the following is correct in a positively skewed distribution?

(a) Mean = Median = Mode (b) Mean < Median < Mode

MCQ No 3.76

If the values of mean, median and mode coincide in a unimodel distribution, then the distribution will be:

(a) Skewed to the left (b) Skewed to the right (c) Multimodal (d) Symmetrical

MCQ No 3.77

A curve that tails off to the right end is called:

(a) Positively skewed (b) Negatively skewed (c) Symmetrical (d) Both (b) and (c)

MCQ No 3.78

The sum of the deviations taken from mean is:

(a) Always equal to zero (b) Some times equal to zero

If a set of data has one mode and its value is less than mean, then the distribution is called:

(a) Positively skewed (b) Negatively skewed (c) Symmetrical (d) Normal

MCQ No 3.80

Taking the relevant root of the product of all non-zero and positive values are called:

(a) Arithmetic mean (b) Geometric mean (c) Harmonic mean (d) Combined mean

MCQ No 3.81

The best average in percentage rates and ratios is:

(a) Arithmetic mean (b) Lower and upper quartiles

MCQ No 3.82

The suitable average for computing average percentage increase in population is:

(a) Geometric mean (b) Harmonic mean (c) Combined mean (d) Population mean

MCQ No 3.83

If 10% is added to each value of variable, the geometric mean of new variable is added by: (a) 10 (b) 1/100 (c) 10% (d) 1.1

MCQ No 3.84

If each observation of a variable X is increased by 20%, then geometric mean is also increased by: (a) 20 (b) 1/20 (c) 20% (d) 100%

MCQ No 3.85

If any value in a series is negative, then we cannot calculate the:

(a) Mean (d) Median (c) Geometric mean (d) Harmonic mean

MCQ No 3.86

Geometric mean for X₁ andX₂ is:

MCQ No 3.87

Geometric mean of 2, 4, 8 is:

(a) 6 (b) 4 (c) 14/3 (d) 8

MCQ No 3.88

Geometric mean is suitable when the values are given as:

(a) Proportions (b) Ratios (c) Percentage rates (d) All of the above

MCQ No 3.89

If the geometric of the two numbers X₁ and X₂ is 9 if X₁=3, then X₂ is equal to: (a) 3 (b) 9 (c) 27 (d) 81

MCQ No 3.90

If the two observations are a = 2 and b = -2, then their geometric mean will be:

(a) Zero (b) Infinity (c) Impossible (d) Negative

Geometric mean of -4, -2 and 8 is:

(a) 4 (b) 0 (c) -2 (d) Impossible

MCQ No 3.92

The ratio among the number of items and the sum of reciprocals of items is called:

(a) Arithmetic mean (b) Geometric mean (c) Harmonic mean (d) Mode

MCQ No 3.93

Harmonic mean for X₁ and X₂ is:

MCQ No 3.94

The appropriate average for calculating the average speed of a journey is:

(a) Median (b) Arithmetic mean (c) Mode (d) Harmonic mean

MCQ No 3.95

Harmonic mean gives less weightage to:

(a) Small values (b) Large values (c) Positive values (d) Negative values

MCQ No 3.96

The harmonic mean of the values 5, 9, 11, 0, 17, 13 is:

(a) 9.5 (b) 6.2 (c) 0 (d) Impossible

MCQ No 3.97

If the harmonic mean of the two numbers X1 and X2 is 6.4 if X2=16, then X1 is:

(a) 4 (b) 10 (c) 16 (d) 20

MCQ No 3.98

If a = 5 and b = -5, then their harmonic mean is:

(a) -5 (b) 5 (c) 0 (d) ∞

MCQ No 3.99

For an open-end frequency distribution, it is not possible to find:

(a) Arithmetic mean (b) Geometric mean (c) Harmonic mean (d) All of the above

MCQ No 3.100

If all the items in a variable are non zero and non negative then:

(a) A.M > G.M > H.M (b) G.M > A.M > H.M (c) H.M > G.M > A.M (d) A.M < G.M < H.M

MCQ No 3.101

The geometric mean of a set of positive numbers X₁, X₂, X₃, ... , X_n is less than or equal to their arithmetic mean but is greater than or equal to their:

(a) Harmonic mean (b) Median (c) Mode (d) Lower and upper quartiles

MCQ No 3.102

Geometric mean and harmonic mean for the values 3, -11, 0, 63, -14, 100 are:

(a) 0 and 3 (b) 3 and -3 (c) 0 and 0 (d) Impossible

If the arithmetic mean and harmonic mean of two positive numbers are 4 and 16, then their geometric mean will be:

(a) 4 (b) 8 (c) 16 (d) 64

MCQ No 3.104

The arithmetic mean and geometric mean of two observations are 4 and 8 respectively, then harmonic mean of these two observations is:

(a) 4 (b) 8 (c) 16 (d) 32

MCQ No 3.105

The geometric mean and harmonic mean of two values are. 8 and 16 respectively, then arithmetic mean of values is:

(a) 4 (b) 16 (c) 24 (d) 128

MCQ No 3.106

Which pair of averages cannot be calculated when one of numbers in the series is zero?

(a) Geometric mean and Median (b) Harmonic mean and Mode

MCQ No 3.107

In a given data the average which has the least value is:

(a) Mean (b) Median (c) Harmonic mean (d) Geometric mean

MCQ No 3.108

If all the values in a series are same, then:

(a) A.M = G.M = H.M (b) A.M ≠ G.M ≠ H.M (c) A.M > G.M > H.M (d) A.M < G.M < H.M

MCQ No 3.109

The averages are affected by change of:

(a) Origin (b) Scale (c) Both (a) and (b) (d) None of the above

UNIT 3:Measures of Dispersion, Skewness and Kurtosis – Range, Quartile Deviation, Mean Deviation, Standard Deviation and their coefficients; Measures of Skewness and Kurtosis. Correlation Analysis – Scatter diagram, Karl Pearson’s coefficient of correlation, Spearman’s ranking method,

MCQ’s of Measures of Dispersion

MCQ No 4.1

The scatter in a series of values about the average is called:

(a) Central tendency (b) Dispersion (c) Skewness (d) Symmetry

MCQ No 4.2

The measurements of spread or scatter of the individual values around the central point is called:

(a) Measures of dispersion (b) Measures of central tendency

MCQ No 4.3

The measures used to calculate the variation present among the observations in the unit of the variable is called:

(a) Relative measures of dispersion (b) Coefficient of skewness

(c) Absolute measures of dispersion (d) Coefficient of variation

MCQ No 4.4

The measures used to calculate the variation present among the observations relative to their average is called:

(a) Coefficient of kurtosis (b) Absolute measures of dispersion

MCQ No 4.5

The degree to which numerical data tend to spread about an average value called:

(a) Constant (b) Flatness (c) Variation (d) Skewness

MCQ No 4.6

The measures of dispersion can never be:

(a) Positive (b) Zero (c) Negative (d) Equal to 2

MCQ No 4.7

If all the scores on examination cluster around the mean, the dispersion is said to be:

(a) Small (b) Large (c) Normal (d) Symmetrical

MCQ No 4.8

If there are many extreme scores on all examination, the dispersion is:

(a) Large (b) Small (c) Normal (d) Symmetric

MCQ No 4.9

Given below the four sets of observations. Which set has the minimum variation?

(a) 46, 48, 50, 52, 54 (b) 30, 40, 50, 60, 70 (c) 40, 50, 60, 70, 80 (d) 48, 49, 50, 51, 52

MCQ No 4.10

Which of the following is an absolute measure of dispersion?

(a) Coefficient of variation (b) Coefficient of dispersion

(c) Standard deviation (d) Coefficient of skewness

MCQ No 4.11

The measure of dispersion which uses only two observations is called:

(a) Mean (b) Median (c) Range (d) Coefficient of variation

The measure of dispersion which uses only two observations is called:

(a) Range (b) Quartile deviation (c) Mean deviation (d) Standard deviation

MCQ No 4.13

In quality control of manufactured items, the most common measure of dispersion is:

(a) Range (b) Average deviation (c) Standard deviation (d) Quartile deviation

MCQ No 4.14

The range of the scores 29, 3, 143, 27, 99 is:

(a) 140 (b) 143 (c) 146 (d) 70

MCQ No 4.15

If the observations of a variable X are, -4, -20, -30, -44 and -36, then the value of the range will be: (a) -48 (b) 40 (c) -40 (d) 48

MCQ No 4.16

The range of the values -5, -8, -10, 0, 6, 10 is:

(a) 0 (b) 10 (c) -10 (d) 20

MCQ No 4.17

If Y = aX ± b, where a and b are any two numbers and a ≠ 0, then the range of Y values will be:

(a) Range(X) (b) a range(X) + b (c) a range(X) – b (d) |a| range(X)

MCQ No 4.18

If the maximum value in a series is 25 and its range is 15, the maximum value of the series is:

(a) 10 (b) 15 (c) 25 (d) 35

MCQ No 4.19

Half of the difference between upper and lower quartiles is called:

(a) Interquartile range (b) Quartile deviation (c) Mean deviation (d) Standard deviation

MCQ No 4.20

If Q3=20 and Q1=10, the coefficient of quartile deviation is:

(a) 3 (b) 1/3 (c) 2/3 (d) 1

MCQ No 4.21

Which measure of dispersion can be computed in case of open-end classes?

(a) Standard deviation (b) Range (c) Quartile deviation (d) Coefficient of variation

MCQ No 4.22

If Y = aX ± b, where a and b are any two constants and a ≠ 0, then the quartile deviation of Y values is equal to:

(a) a Q.D(X) + b (b) |a| Q.D(X) (c) Q.D(X) – b (d) |b| Q.D(X)

MCQ No 4.23

The sum of absolute deviations is minimum if these deviations are taken from the:

(a) Mean (b) Mode (c) Median (d) Upper quartile

MCQ No 4.24

The mean deviation is minimum when deviations are taken from:

(a) Mean (b) Mode (c) Median (d) Zero

If Y = aX ± b, where a and b are any two numbers but a ≠ 0, then M.D(Y) is equal to:

(a) M.D(X) (b) M.D(X) ± b (c) |a| M.D(X) (d) M.D(Y) + M.D(X)

MCQ No 4.26

The mean deviation of the scores 12, 15, 18 is:

(a) 6 (b) 0 (c) 3 (d) 2

MCQ No 4.27

Mean deviation computed from a set of data is always:

(a) Negative (b) Equal to standard deviation

MCQ No 4.28

The average of squared deviations from mean is called:

(a) Mean deviation (b) Variance (c) Standard deviation (d) Coefficient of variation

MCQ No 4.29

The sum of squares of the deviations is minimum, when deviations are taken from:

(a) Mean (b) Mode (c) Median (d) Zero

MCQ No 4.30

Which of the following measures of dispersion is expressed in the same units as the units of observation?

(a) Variance (b) Standard deviation

MCQ No 4.31

Which measure of dispersion has a different unit other than the unit of measurement of values:

(a) Range (b) Standard deviation (c) Variance (d) Mean deviation

MCQ No 4.32

Which of the following is a unit free quantity:

(a) Range (b) Standard deviation (c) Coefficient of variation (d) Arithmetic mean

MCQ No 4.33

If the dispersion is small, the standard deviation is:

(a) Large (b) Zero (c) Small (d) Negative

MCQ No 4.34

The value of standard deviation changes by a change of:

(a) Origin (b) Scale (c) Algebraic signs (d) None

MCQ No 4.35

The standard deviation one distribution dividedly the mean of the distribution and expressing in percentage is called:

(a) Coefficient of Standard deviation (b) Coefficient of skewness

MCQ No 4.36

The positive square root of the mean of the squares of the cleviations of observations from their mean is called:

(a) Variance (b) Range (c) Standard deviation (d) Coefficient of variation

The variance is zero only if all observations are the:

(a) Different (b) Square (c) Square root (d) Same

MCQ No 4.38

The standard deviation is independent of:

(a) Change of origin (b) Change of scale of measurement

MCQ No 4.39

If there are ten values each equal to 10, then standard deviation of these values is: (a) 100 (b) 20 (c) 10 (d) 0

MCQ No 4.40

If X and Y are independent random variables, then S.D(X ± Y) is equal to:

(a) S.D(X) ± S.D(Y) (b) Var(X) ± Var(Y) (c) (d)

MCQ No 4.41

S.D(X) = 6 and S.D(Y) = 8. If X and Yare independent random variables, then S.D(X-Y) is: (a) 2 (b) 10 (c) 14 (d) 100

MCQ No 4.42

For two independent variables X and Y if S.D(X) = 1 and S.D(Y) = 3, then Var(3X - Y) is equal to: (a) 0 (b) 6 (c) 18 (b) 12

MCQ No 4.43

If Y = aX ± b, where a and b are any two constants and a ≠ 0, then Vat (Y) is equal to:

(a) a Var(X) (b) a Var(X) + b (c) a² Var(X) – b (d) a² Var(X)

MCQ No 4.44

If Y = aX + b, where a and b are any two numbers but a ≠ 0, then S.D(Y) is equal to:

(a) S.D(X) (b) a S.D(X) (c) |a| S.D(X) (d) a S.D(X) + b

MCQ No 4.45

The ratio of the standard deviation to the arithmetic mean expressed as a percentage is called:

(a) Coefficient of standard deviation (b) Coefficient of skewness

MCQ No 4.46

Which of the following statements is correct?

(a) The standard deviation of a constant is equal to unity

(b) The sum of absolute deviations is minimum if these deviations are taken from the mean.

(d) The variance is positive quantity and is expressed in square of the units of the observations

Which of the following statements is false?

(a) The standard deviation is independent of change of origin

(b) If the moment coefficient of kurtosis β₂ = 3, the distribution is mesokurtic or normal.

(c) If the frequency curve has the same shape on both sides of the centre line which divides the curve into two equal parts, is called a symmetrical distribution.

(d) Variance of the sum or difference of any two variables is equal to the sum of their respective variances

MCQ No 4.48

If Var(X) = 25, then is equal to:

(a) 15/2 (b) 50 (c) 25 (d) 5

MCQ No 4.49

To compare the variation of two or more than two series, we use

(a) Combined standard deviation (b) Corrected standard deviation

(c) Coefficient of variation (d) Coefficient of skewness

MCQ No 4.50

The standard deviation of -5, -5, -5, -5, 5 is:

(a) -5 (b) +5 (c) 0 (d) -25

MCQ No 4.51

Standard deviation is always calculated from:

(a) Mean (b) Median (c) Mode (d) Lower quartile

MCQ No 4.52

The mean of an examination is 69, the median is 68, the mode is 67, and the standard deviation is 3. The measures of variation for this examination is:

(a) 67 (b) 68 (c) 69 (d) 3

MCQ No 4.53

The variance of 19, 21, 23, 25 and 27 is 8. The variance of 14, 16, 18, 20 and 22 is:

(a) Greater than 8 (b) 8 (c) Less than 8 (d) 8 - 5 = 3

MCQ No 4.54

In a set of observations the variance is 50. All the observations are increased by 100%. The variance of the increased observations will become:

(a) 50 (b) 200 (c) 100 (d) No change

MCQ No 4.55

Three factories A, B, C have 100, 200 and 300 workers respectively. The mean of the wages is the same in the three factories. Which of the following statements is true?

(a) There is greater variation in factory C.

(b) Standard deviation in. factory A is the smallest.

(d) None of the above

An automobile manufacturer obtains data concerning the sales of six of its deals in the last week of 1996. The results indicate the standard deviation of their sales equals 6 autos. If this is so, the variance of their sales equals:

(a) (b) 6 (c)

(d) 36

MCQ No 4.57

If standard deviation of the values 2, 4, 6, 8 is 2.236, then standard deviation of the values 4, 8,12, 16 is:

(a) 0 (b) 4.472 (c) 4.236 (d) 2.236

MCQ No 4.58

Var(X) = 4 and Var(Y) =9. If X and Y are independent random variable then Var(2X + Y) is: (a) 13 (b) 17 (c) 25 (d) -1

MCQ No 4.59

If = Rs.20, S= Rs.10, then coefficient of variation is:

(a) 45% (b) 50% (c) 60% (d) 65%

MCQ No 4.60

Which of the following measures of dispersion is independent of the units employed?

(a) Coefficient of variation (b) Quartile deviation

MCQ No 4.61

In sheppard’s correction µ₂ is equal to:

MCQ No 4.62

The moments about mean are called:

(a) Raw moments (b) Central moments (c) Moments about origin (d) All of the above

MCQ No 4.63

The moments about origin are called:

(a) Moments about zero (b) Raw moments (c) Both (a) and (b) (d) Neither (a) nor (b)

MCQ No 4.64

All odd order moments about mean in a symmetrical distribution are:

(a) Positive (b) Negative (c) Zero (d) Three

MCQ No 4.65

The second moment about arithmetic mean is 16, the standard deviation will be: (a) 16 (b) 4 (c) 2 (d) 0

MCQ No 4.66

The first and second moments about arbitrary constant are -2 and 13 respectively, The standard deviation will be:

(a) -2 (b) 3 (c) 9 (d) 13

Moment ratios β₁ and β₂ are:

(a) Independent of origin and scale of measurement

(b) Expressed in original unit of the data

(c) Unit less quantities

(d) Both (a) and (c)

MCQ No 4.68

The first moment about X = 0 of a distribution is 12.08. The mean is:

(a) 10.80 (b) 10.08 (c) 12.08 (d) 12.88

MCQ No 4.69

First two moments about the value 2 of a variable are 1 and 16. The variance will be:

(a) 13 (b) 15 (c) 16 (d) Difficult to tell

MCQ No 4.70

The first three moments of a distribution about the mean are 1, 4 and 0. The distribution is:

(a) Symmetrical (b) Skewed to the left (c) Skewed to the right (d) Normal

MCQ No 4.71

If the third central is negative, the distribution will be:

(a) Symmetrical (b) Positively skewed (c) Negatively skewed (d) Normal

MCQ No 4.72

If the third moment about mean is zero, then the distribution is:

(a) Positively skewed (b) Negatively skewed (c) Symmetrical (d) Mesokurtic

MCQ No 4.73

Departure from symmetry is called:

(a) Second moment (b) Kurtosis (c) Skewness (d) Variation

MCQ No 4.74

In a symmetrical distribution, the coefficient of skewness will be:

(a) 0 (b) Q₁ (c) Q₃ (d) 1

MCQ No 4.75

The lack of uniformity or symmetry is called:

(a) Skewness (b) Dispersion (c) Kurtosis (d) Standard deviation

MCQ No 4.76

For a positively skewed distribution, mean is always:

(a) Less than the median

(c) Greater than the mode

(b) Less than the mode

(d) Difficult to tell

MCQ No 4.77

For a symmetrical distribution: (a) β₁ > 0 (b) β₁ < 0

(c) β₁ = 0

(d) β₁ = 3

MCQ No 4.78

If mean=50, mode=40 and standard deviation=5, the distribution is:

(a) Positively skewed (b) Negatively skewed (c) Symmetrical (d) Difficult to tell

If mean=25, median=30 and standard deviation=15, the distribution will be:

(a) Symmetrical (b) Positively skewed (c) Negatively skewed (d) Normal

MCQ No 4.80

If mean=20, median=16 and standard deviation=2, then coefficient of skewness is: (a) 1 (b) 2 (c) 4 (d) -2

MCQ No 4.81

If mean=10, median=8 and standard deviation=6, then coefficient of skewness is:

(a) 1 (b) -1 (c) 2/6 (d) 2

MCQ No 4.82

If the sum of deviations from median is not zero, then a distribution will be:

(a) Symmetrical (b) Skewed (c) Normal (d) All of the above

MCQ No 4.83

In case of positively skewed distribution, the extreme values lie in the:

(a) Middle (b) Left tail (c) Right tail (d) Anywhere

MCQ No 4.84

Bowley's coefficient of skewness lies between:

(a) 0 and 1 (b) 1 and +1 (c) -1 and 0 (d) -2 and +2

MCQ No 4.85

In a symmetrical distribution, Q₃ – Q₁ = 20, median = 15. Q₃ is equal to: (a) 5 (b) 15 (c) 20 (d) 25

MCQ No 4.86

Which of the following is correct in a negatively skewed distribution?

(a) The arithmetic mean is greater than the mode

(b) The arithmetic mean is greater than the median

(d) (Q₃ – Median) < (Median – Q₁)

MCQ No 4.87

The lower and upper quartiles of a distribution are 80 and 120 respectively, while median is 100. The shape of the distribution is:

(a) Positively skewed (b) Negatively skewed (c) Symmetrical (d) Normal

MCQ No 4.88

In a symmetrical distribution Q₁ = 20 and median= 30. The value of Q₃ is: (a) 50 (b) 35 (c) 40 (d) 25

MCQ No 4.89

The degree of peaked ness or flatness of a unimodel distribution is called:

(a) Skewness (b) Symmetry (c) Dispersion (d) Kurtosis

MCQ No 4.90

For a leptokurtic distribution, the relation between second and fourth central moment is:

For a platydurtic distribution, the relation between and is:

MCQ No 4.92

For a mesokurtic distribution, the relation between fourth and second mean moment is:

MCQ No 4.93

The second and fourth moments about mean are 4 and 48 respectively, then the distribution is:

(a) Leptokurtic (b) Platykurtic (c) Mesokurtic or normal (d) Positively skewed

MCQ No 4.94

In a mesokurtic or normal distribution, µ₄ = 243. The standard deviation is: (a) 81 (b) 27 (c) 9 (d) 3

MCQ No 4.95

The value of β₂ can be:

(a) Less than 3 (b) Greater than 3 (c) Equal to 3 (d) All of the above

MCQ No 4.96

In a normal (mesokurtic) distribution:

(a) β₁=0 and β₂=3 (b) β₁=3 and β₂=0 (c) β₁=0 and β₂>3 (d) β₁=0 and β₂<3

MCQ No 4.97

Any frequency distribution, the following empirical relation holds:

(a) Quartile deviation = Standard deviation

(b) Mean deviation = Standard deviation

Statical Methods B.COM SEM 3 Multiple Choice Questions Topic Wise

MCQ No 3.1

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MCQ No 3.86