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.

Answer:

Question 14:

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

Answer:

Question 15:

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

Mean and Variance of the Frequency
Mean and Variance of the Frequency

Answer:

Long Answer Type

Question 16:

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

Class Interval and Frequency
Class Interval and Frequency

Class Interval

Frequency

Answer:

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

The Frequency Distribution
The frequency distribution

Class Interval

Mid Value

Frequency

Total

Here mean,

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

The Above Table with More Columns
The above table with more Columns

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:

Table of Calculate the Mean Deviation
Table of Calculate the mean deviation

Class Interval

Frequency

Answer:

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

The Frequency Distribution
The frequency distribution

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,

Table with More Columns
Table with more columns

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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