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CLASS_11_MATHS_SOLUTIONS_NCERT

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Class XI Chapter 15 – Statistics Maths<br />

______________________________________________________________________________<br />

Question 3:<br />

The mean and standard deviation of six observations are 8 and 4, respectively. If each<br />

observation is multiplied by 3, find the new mean and new standard deviation of the resulting<br />

observations.<br />

Solution 3:<br />

Let the observations be x1, x2, x3, x4, x5, and x6.<br />

It is given that mean is 8 and standard deviation is 4.<br />

x1 x2 x3 x4 x5 x6<br />

Mean, x= 8 ……..(1)<br />

6<br />

If each observation is multiplied by 3 and the resulting observations are y<br />

i<br />

,, then<br />

1<br />

y1 3 x1 i. e., x1 y1,for i=1 to 6<br />

3<br />

y1 y2 y3 y4 y5 y6<br />

New Mean, y=<br />

6<br />

3x1 x2 x3 x4 x5 x6<br />

<br />

=<br />

6<br />

38 .... Using 1<br />

28<br />

1<br />

6<br />

2<br />

Standard deviation, = x1<br />

x<br />

n i1<br />

2 1<br />

6<br />

2<br />

4 x1<br />

x<br />

6 i1<br />

6<br />

i1<br />

2<br />

x<br />

x 96 ... 2<br />

<br />

1<br />

From (1) and (2), it can be observed that,<br />

y 3x<br />

1<br />

x y<br />

3<br />

Substituting the values of x<br />

1 and x in (2), we obtain<br />

6<br />

1 1 <br />

<br />

y1<br />

y 96<br />

3 3<br />

<br />

<br />

i1<br />

6<br />

i1<br />

<br />

y y 864<br />

1<br />

<br />

2<br />

2<br />

1 <br />

Therefore, variance of new observations = 864 144<br />

6<br />

<br />

<br />

Hence, the standard deviation of new observations is 144 12<br />

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