Question

The mean of 9 observations is 35 .Lately it is found that the observations 8 was misread as 18.find the correct mean

Answer 1

Given :-

• The mean of 9 observations is 35.

• Correct observation is 8.

• Incorrect observation is 18.

To find :-

• The correct mean

$\large\underline\purple{\bold{Solution :- }}$

Given that,

• Number of observations = 9

• Mean of observations = 35

We know that,

• Mean of 'n' observations is given by

$\rm :\implies\: \boxed{ \pink{ \bf \: mean \: ( \overline{x}) \: = \tt \: \dfrac{\sum_{j=1}^n x_j}{n} }}$

So,

$\rm :\implies\:35 = \dfrac{\sum_{j=1}^9 x_j}{9}$

$\rm :\implies\:\sum_{j=1}^9 x_j \: = \: 35 \times 9$

$\boxed{ \red{\rm :\implies\:\sum_{j=1}^9 x_j = 315}}$

Now,

It is found that,

• Correct observation = 8

• Incorrect observation = 18

So correct sum is given by

$\rm :\implies\:correct\sum_{j=1}^9 x_j = 315 - 18 + 8$

$\rm :\implies\:correct \: \sum_{j=1}^9 x_j \: = \: 305$

So,

Now,

• Correct mean is

$\rm :\implies\: \overline{x} \: = \: \dfrac{correct \: \sum_{j=1}^9 x_j \:}{9}$

$\rm :\implies\: \overline{x} \: = \dfrac{305}{9}$

$\large \boxed{ \green{\rm :\implies\: \overline{x} \: = 33.89}}$