# MCQs Basic Statistics 3

This test contains multiple choice questions on measure of dispersion such as range, variance, standard deviation, mean deviation, characteristics and properties of measure of dispersion, absolute measure of dispersion or relative measure of dispersion etc.

1) A measure of dispersion is always ________

A) Zero
B) Positive
C) Negative
D) Infinity

2) Which of these is a relative measure of dispersion

A) Standard Deviation
B) Variance
C) Coefficient of Variation
D) None of these

3) The measure of dispersion is changed by a change of

A) Origin
B) Scale
C) Algebraic Signs
D) None

4) Mean Deviation, Variance and Standard Deviation of the values 4, 4, 4, 4, 4, 4 is

A) 4
B) 8
C) 2
D) 12
E) 0

5) The mean deviation of the values, 18, 12, 15 is

A) 6
B) Zero
C) 3
D) 2

6) The sum of squares of deviation is least if measure from

A) Mean
B) Mode
C) Median
D) Variance

7) The sum of squared deviations of a set of n values from their mean is

A) Zero
B) Maximum
C) Least
D) None

8) Variance is always calculated from

A) Mode
B) Variance
C) Geometric Mean
D) Median
E) Mean

9) Lowest value of variance can be

A) 1
B) -1
C) 3
D) -3
E) 0

10) The variance of a constant is

A) Zero
B) Constant
C) a
D) None

11) Variance remains unchanged by change of

A) Origin
B) Scale
C) Both
D) None of these

12) $Var(2X+3)\,$ is

A) 5 Var(X)
B) 4 Var(X)
C) 4 Var(X)+3
D) 5 Var(X)+3

13) If a and b are two constants, then $Var(a + bX)\,$ is

A) $a\pm b Var(X)$
B) $Var(a) \pm Var(X)$
C) $\pm b Var(X)$
D) $b^2 Var(X)$
E) $(a \pm b) Var(X)$

14) Suppose for 40 observations, the variance is 50. If all the observations are increased by 20, the variance of these increased observation will be

A) 50
B) 70
C) 50/20
D) 50-20 = 30
E) 50

15) Standard deviation is calculated from the Harmonic Mean (HM)

A) Always
B) Sometimes
C) Never
D) None of these

16) The variance of 5 numbers is 10. If each number is divided by 2, then the variance of new numbers is

A) 20
B) 5
C) 2.5
D) 5.5
E) 0

17) If X and Y are independent then SD (X − Y) is

A) $SD(X)-SD(Y)$
B) $SD(X)+SD(Y)$
C) $\sqrt{SD(X)+SD(Y)}$
D) $\sqrt{Var(X)+Var(Y)}$

18) If Y=−8X  5 and SD of X is 3, then SD of Y is

A) 8
B) 3
C) 5
D) 24
E) None

19) The standard deviation is always _________ than mean deviation

A) Greater
B) Less
C) Equal
D) None

20) If the standard deviation of the values 2, 4, 6, 8 is 2.33, then the standard deviation of the values 4, 6, 8, 10 is

A) 0
B) 2.58
C) 5
D) 4.66
E) 2.33

21) For a symmetrical distribution approximately 68% of the cases are included between

A) $\overline{X}-S\,$ and $\overline{X}+S$
B) $\overline{X}-2S\,$ and $\overline{X}+2S$
C) $\overline{X}-3S\,$ and $\overline{X}+3S$
D) None of these

22) The percentage of values lies between $\overline{X}\pm 2 SD\,$ is

A) 68.26%
B) 95.45%
C) 99.7%
D) 65%
E) 99%

23) The measure of Dispersion can never be

A) Positive
B) Negative
C) 0
D) 1

24) If all values are same then the measure of dispersion will be

A) 1
B) 0
C) Mean
D) Mode
E) Median

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## MCQs about Measure of Dispersion I

This test contains MCQS about Measure of Dispersion/ Variation such as Standard Deviation, Variance, Mean Deviation, Coefficient of Variation, Moments, Symmetry and Skewness, Kurtosis, Quartiles Deviations, Range etc.
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#### Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics. Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan. Like Applied Statistics and Mathematics and Statistical Computing. Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis etc.