# NCERT Class 11-Math's: Exemplar Chapter –15 Statistics Part 5

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Question 13:

Mean and standard deviation of items are and , respectively. Find the sum of all the item and the sum of the squares of the items.

Question 14:

If for a distribution and the total number of item is , find the mean and standard deviation.

Question 15:

Find the mean and variance of the frequency distribution given below:

## Long Answer Type

Question 16:

Calculate the mean deviation about the mean for the following frequency distribution:

 Class Interval Frequency

Given: the frequency distribution

To find: the mean deviation about the mean

Let us make a table of the given data and append other columns after calculations

 Class Interval Mid Value Frequency Total

Here mean,

So the above table with more columns is as shown below,

 Class Interval Mid Value Frequency Total

Hence Mean Deviation becomes,

Therefore, the mean deviation about the mean of the distribution is

Question 17:

Calculate the mean deviation from the median of the following data:

 Class Interval Frequency

Given: the frequency distribution

To find: the mean deviation from the median

Let us make a table of the given data and append other columns after calculations

 Class Interval Mid Value Frequency Cumulative Frequency (c.f) Total

Now, here , which is even.

Here median class term,

This observation lie in the class interval , so median can be written as,

Here , , and , substituting these values, the above equation becomes,

So the above table with more columns is as shown below,

 Class Interval Mid Value Frequency Total

Hence Mean Deviation becomes,

Therefore, the mean deviation about the median of the distribution is 7

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