# NCERT Class 11-Math՚s: Exemplar Chapter – 15 Statistics Part 11 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 23**:

While calculating the mean and variance of readings, a student wrongly used the reading for the correct reading . He obtained the mean and variance as and respectively. Find the correct mean and the variance.

**Answer**:

Given: While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively

To find: the correct mean and the variance.

As per given criteria,

Number of reading,

Mean of the given readings before correction,

But we know,

Substituting the corresponding values, we get

It is said one reading was wrongly taken as ,

So

So the correct mean after correction is

Also given the variance of the 10 readings is 16 before correction,

i.e.. ,

But we know

Substituting the corresponding values, we get

It is said one reading 25 was wrongly taken as 52, so

So the correct variance after correction is

Hence the corrected mean and variance and respectively.

## Objective Type Questions

### Choose the Correct Answer Out of the Given Four Options in Each of the Exercises 24 to 39 (M. C. Q.)

**Question 24**

The mean deviation of the data from the mean is

(A)

(B)

(C)

(D)

**Answer: (B)**

**Question 25**:

Mean deviation for n observations from their mean x is given by

(A)

(B)

(C)

(D)

**Answer: (B)**

**Question 26**:

When tested, the lives (in hours) of bulbs were noted as follows:

The mean deviations (in hours) from their mean is

(A)

(B)

(C)

(D)

**Answer: (B)**