# SSC

Explore popular questions from Statistics & Data Interpretation for SSC. This collection covers Statistics & Data Interpretation previous year SSC questions hand picked by experienced teachers.

## Statistics

Statistics & Data Interpretation

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Q 1. If the sum of 11 consecutive natural numbers is 2761, then the middle number is:

A

249

B

250

251

D

252

##### Explanation

Let the first natural number be x

According to the question

x+x+1x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9+x+10=2761

=> 11x + 55 = 2761

x = {tex} \frac{2761 - 55}{11} = 246 {/tex}

Middle number = x + 5 = 246 + 5 = 251

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Q 2. The mean weight of 9 items is 15. If one more item is added to the series, the mean 16. The value of 10th item is

A

35

B

30

25

D

20

##### Explanation

Total weight of 9 items = 15 x 9 = 135

and total weigth of 10 items = 16 X 10 = 160

Therefore, weight of 10 items = 160 - 135 = 25

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Q 3. The mean of 12 items is {tex} \bar{X} {/tex} . If the first term is increased by 1, second by 2 and so on, then the new mean is

A

{tex} \overline{X}+n {/tex}

B

{tex} \overline{X}+\frac{n}{2} {/tex}

{tex} \overline{X}+\frac{n+1}{2} {/tex}

D

none of these

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Q 4. If the mean of n observation {tex} 1^{2},\ 2^{2},\ 3^{2},........n^{2} {/tex}, is {tex} \frac{46}{11}n {/tex}, then n is equal to

11

B

12

C

23

D

22

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Q 5. The value of mean, median and mode coincides, then the distribution is

A

Positive skewness

Symmetrical distribution

C

Negative skewness

D

All of these

##### Explanation

If mean, median and mode coincides, then there is a symmetrical distribution.

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Q 6. For a series the value of mean deviation is 15, the most likely value of its quartile deviation is

12.5

B

11.6

C

13

D

9.7

##### Explanation

Since,

{tex} MD = \frac{4}{5}\sigma,\ QD=\frac{2}{3}\sigma {/tex}

{tex} \therefore\ \frac{MD}{QD} = \frac{6}{5} {/tex}

=> {tex} QD = \frac{5}{6} \left(MD\right)=\frac{5}{6} \left(15\right)=12.5 {/tex}

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Q 7. If {tex} \overline{x} {/tex} is the arithmetic mean of n independent variates {tex} x_{1},\ x_{2},\ x_{3}.....,\ x_{n} {/tex} each of the standard deviation {tex} \sigma {/tex}, the variance {tex} \overline{x} {/tex} is

{tex} \frac{\sigma^{2}}{n} {/tex}

B

{tex} \frac{n\sigma^{2}}{2} {/tex}

C

{tex} \frac{\left(n+1\right)\sigma^{2}}{3} {/tex}

D

None of these

##### Explanation

We have, {tex} \overline{x} = \frac{1}{n}\sum^{n}_{i=1}x_{i} {/tex}

Therefore, {tex} var \left(\overline{x}\right) = \frac{1}{n^{2}}\left[ \sum^{n}_{i=1} var \left(x_{j}\right)+2\sum^{n}_{i \neq j} cov \left(x_{i},\ x_{j}\right) \right] {/tex}

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Q 8. Calculate the mean for the following frequency distribution.

 x: 10-20 20-30 30-40 40-50 50-60 60-70 70-80 f: 6 8 9 10 7 5 15

A

54.32

B

62.24

48.16

D

42.14

##### Explanation

 x f m {tex} x' = \frac{m-A}{i} {/tex} fx' 10-20 6 15 -3 -18 20-30 8 25 -2 -16 30-40 9 35 -1 -9 40-50 10 45 0 0 50-60 7 55 1 7 60-70 5 65 2 10 70-80 15 75 3 45 {tex} \sum =60 {/tex} {tex} \sum fx'=19 {/tex}

m - middle point of the interval.

i. -differene of the class interval.

A = 45

Arithmetic mean {tex} \overline{x} = A+ \frac{\sum f'x}{\sum f}i {/tex}

= {tex} 45+\frac{19}{60} \times 10 {/tex}

={tex} 45+3.16 = 48.16 {/tex}