# Free Measures of Dispersion 03 Practice Test - 11th Grade - Commerce

### Question 1

The square root of

#### SOLUTION

Solution :Standard deviation is the square root of variance.

### Question 2

The distribution of weights of 50 students in a class is as follows.

Weight (kg)40−4545−5050−5555−6060−6565−70No. of students371112107

Calculate the standard deviation using the step deviation method.

#### SOLUTION

Solution :D

Let the assumed mean be 52.5 i.e. A = 52.5 and the dividing factor (c) be 5.

XFDD′=DcFD′FD′242.53−10−2−61247.57−5−1−7752.511000057.51251121262.510102204067.571532163∑F=50∑FD′=40∑FD′2=134

σ=√∑FD′2∑F−(∑FD′∑F)2×c=√13450−(4050)2×5=√2.68−0.64×5=√2.04×5=1.428×5=7.14

### Question 3

Relative measures of dispersion have the same units as that of the observations in the data. State true or false.

#### SOLUTION

Solution :B

Relative measures are ratios and have no units.

### Question 4

Find the coefficient of mean deviation about median for the following cumulative frequency distribution:

xfrequencyCumulative frequency221134233925458135482156930684347843884240

0.187

0.203

0.215

0.224

#### SOLUTION

Solution :A

Here, the sum of frequencies, n = 40, which is even.

So, the median terms will be the n2th and the (n2+1)th observations, i.e. the 20th and the 21st observations.

Both the 20th and the 21st observations are 54.

So, the median term, M= 54.

Deviations from the median are tabulated below

XFD=|X−M|FD22132323422040392153045897254800569218684145678424968423060 ∑F=40∑FD=404

M.D(M)=40440=10.1

Coefficient of M.D(M)=M.D(M)Median=10.154=0.187

### Question 5

The following are the scores of Adil and Kratu in 5 subjects. Adil's scores are out of 10 and Kratu's are out of 50.

Adil: 7, 9, 6, 8, 4

Kratu: 36, 44, 49, 41, 25

Compare the variability in scores using the coefficient of variation.

#### SOLUTION

Solution :A

MeanA=7+9+6+8+45=6.8

MeanK=36+44+49+41+255=39

σA=√0.22+2.22+0.82+1.22+2.825=√2.96=1.72

σK=√32+52+102+22+1425=√66.8=8.17

C.O.VA=1.726.8×100=25.29%

C.O.VK=8.1739×100=20.95%

Hence, Adil's scores have higher variability

### Question 6

Inter-quartile range =

#### SOLUTION

Solution :C

Inter−quartile range=Q3−Q1

### Question 7

Number of goals scored by Ronaldo in champions league for past 10 years are as follows. {1, 3, 8, 4, 7, 6, 10, 12, 17, 10} Find the mean deviation about the mean.

3

3.6

4

4.4

#### SOLUTION

Solution :B

Mean=1+3+8+4+7+6+10+12+17+1010

¯X=7810=7.8

∑|X−7.8|=6.8+4.8+0.2+3.8 +0.8+1.8+2.2+4.2+9.2+2.2=36

∴ Mean deviation=3610=3.6

### Question 8

If the coefficient of variation and standard deviation of a distribution are 2 and 0.4 respectively, then mean of the distribution is

40

20

10

8

#### SOLUTION

Solution :B

C.V=2;σ=0.4(given)C.V=100×s.dmean2=100×0.4meanMean=402=20

### Question 9

If the S.D of a set of observations is 4 and if each observation is divided by 4, the S.D of the new set of observations will be

4

3

2

1

#### SOLUTION

Solution :D

We know that if we multiply all numbers of a set by a constant "k" then the mean of these numbers will also be a multiple of the old mean.

And the variance of these numbers will be multiple of "k2".

Since standard deviation is nothing but the square root of variance, s.d will be multiple of "k" of the old standard deviation.

We are given the s.d was 4.

So after multiplying each observation by (1/4), the s.d will also be multiplied by (1/4), thus giving the value = 4×14 = 1

### Question 10

The coefficient of variation of a distribution is

100×σ¯X

100×¯Xσ

100×σ2¯X

σ¯X

#### SOLUTION

Solution :A

C.V. is given byC.V=100×σ¯X