MCQs on Descriptive Statistics | Stat Wiki

 STATISTICS AND STATISTICAL METHODS of DESCRIPTIVE STATISTICS

 

This chapter is consist of 

Frequency distribution, 
Graphical representation of distributions, 
Central tendency, 
Dispersion, 
Coefficient of  variation.

1._________________ is used to measure the symmetrical/asymmetrical patterns of a distribution

a)Mode
b)Median
c)Kurtosis
d)Skewness

Ans: Skewness

2.Which tool measures the flatness of a distribution?

a)Mode
b)Median
c)Kurtosis
d)Skewness

Ans: Kurtosis

3.15-19,20-24,25-29,30-34,...... is it a inclusive type of classification?

a)true
b)false

Ans: True

4.Can we draw histogram for any kinds of distribution?

a)continuous distribution
b)discrete  distribution
c)both 

Ans: continuous distribution

Also Read: See the MCQs on Expectation

5.What is the value of the mean if the the observations(1,2,3,4,5) and the frequencies are same for the each observations(eg. for observation 1 the frequency is 1 and so on)

a)10
b)11
c)12
d)13

Ans: 11

hint: $\small\frac{(1\times 1)+(2 \times 2)+ (3 \times 3)+ (4\times 4)+(5\times 5)}{5}$ =11

6.The average salary of male employees in a firm was Rs. 5200 and that of females was Rs. 4200. The mean salary of all the employees was Rs. 5000. Find the percentage of male and employees.

a)male: 80% and female: 20%
b)male: 70% and female: 30%
c)male: 60% and female: 40%

Ans: male: 80% and female: 20%

hint: let, there is x males and y females

clearly, $\small\frac{(x\times 5200)+(y \times 4200) }{x+y}$ =5200

7.Which is correct?

a)3 median= 2 mean + mode
b)2 median= 3 mean + mode 

c)  median= 3 mean + 2 mode

Ans: 3 median= 2 mean + mode

8.When you can use mode as mean or median?

a)Symmetrical distribution
b)Asymmetrical distribution
c)None

Ans: Symmetrical distribution

Read Also: MCQs on random variables and distribution functions

9. The geometric mean of  10 observations on a certain variable was 16.2. It was discovered that one of the observations was wrongly recorded as 12.9; in fact it was 21.9. What will be the corrected geometric mean?

a)17.08
b)18.08
c)19.18
d)20.08

 

Ans: 17.08 

 

Hint: if $\small x_{1}$ wrongly copied as $\small y_{1}$ then the corrected geometric mean $\small {G}'$ is $\small {G}'\tfrac{x_{1}}{y_{1}}$  

10. What is the suitable measure of finding the means of speed, price or other variables where rate represents a ratio?

a) Harmonic mean
b) Geometric mean
c) Arithmetic mean

Ans:  Harmonic mean

11.What will be the value of frequency for  $P_{27}$ , $Q_{3}$ , $D_{4}$ if the the total frequency N =256?

a) $\small P_{27}$ , $Q_{3}$ , $D_{4}$ = 69.12, 192, 102.4
b) $\small P_{27}$ , $Q_{3}$ , $D_{4}$ =192, 102.4, 69.12
c) None of these

Ans: $\small P_{27}$ , $Q_{3}$ , $D_{4}$ = 69.12, 192, 102.4

Hint:  

$\small P_{27}$= $\small \frac{27}{100}\times  N$ 

$\small Q_{3}$=  $\small \frac{3}{4}\times  N$

$\small D_{4}$=  $\small \frac{4}{10}\times  N$

12. What will be the range of these observations 2,9,8,7,63.95,101,5,13

a)5
b)95
c)99
d)75

Ans: 99

Read Also: MCQ's on Probability

hint: Range: highest observation - lowest observation

13.

0-10	10-20	20-30	30-40	40-50	50-60	60-70
6	5	8	15	7	6	3

What will be the value of Quartile deviation and Mean deviation?

a)45,13
b)48,14
c)49,15
d)50,16

Ans: 45,13 (approx)

[ comment below to get the answer] 

14. Is it true or false?

"Variance is the minimum value of mean square deviation"

a)True
b)False

Ans: True 

15. For a group of 200 candidates, the mean and standard deviations of scores were found to be 40 and 15 respectively. Later on it was discovered that the scores 43 and 35 were misread as 34 and 53. Find the corrected mean and Standard deviation. 

a)39.995, 224.14
b)39.995,14.97
c)48.995,224.14
d)48.995,14.97

 

Ans: 39.995,14.97

 

[ comment below to get the answer]

16.Verify the statement 

S.D > M.D 

a)True
b)False

Ans: True

17. Find the coefficient of variation if the $\bar{x}$ =50 and $\sigma$ =4?

Ans: 8

18. Which statement is correct?  

a)$\small \mid S_{k} \mid \leqslant 3$

b)$\small \mid S_{k} \mid \leqslant 2$

c)$\small \mid S_{k} \mid \leqslant 1$

Ans: $\small \mid S_{k} \mid \leqslant 3$

19.If a distribution has a variance of 16 and the mean is 10. and the skewness is 1.Then what will be the value of third order moment? 

a)64 

b)56

c)36

d)25

Ans: 64

[ comment below to get the answer] 

20. If the value of the $\small\beta _{2}$ is >3  and the $\small\gamma _{1}$ is less than 1,then what will be shape of the curve?

a)negatively skew and leptokurtic
b)positively skew and leptokurtic
c)negatively skew and platykurtic
d)positively skew and mesokurtic

Ans:negatively skew and leptokurtic

Do your self:

21. What is the algebraic sum of the deviations of a set of n values from their arithmetic mean? Ans: 

22.What is the most stable measure of central tendency among mean, median,mode?

Ans: Mean

23.10 is the mean of 7 observations and the mean of  3 observation is 5.What is the value of combine mean?

Ans: 8.5

 

24. The arithmetic man of 1,2,3,........2n is ______________.

Ans: $\small\frac{2n+1}{1}$

25. The point of intersection of the less than and the more than ogive corresponds to which central tendency?

Ans: Median

26. What is relation between A.M,H.M,G.M?

Ans: $\small A.M\geq G.M \geq H.M$

 

27.  Which order moment is zero for a symmetric distribution?

Ans: Third order moment

 

28. What is relation between mean, median and mode for a symmetric distribution?

Ans: Mean=Median=Mode

 

29.What do you mean by lesser Coefficient of variation?

Ans: The variable is consistent then other variables.

 

30. What is the minimum value of mean square error?

Ans: Variance.