# NCERT Class 11-Math՚s: Exemplar Chapter – 15 Statistics Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 18:

Determine the mean and standard deviation for the following distribution:

 Marks 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Frequency 1 6 6 8 8 2 2 3 0 2 1 0 0 0 1

Given: the frequency distribution

To find: the mean and standard deviation

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

 Marks Frequency 2 1 3 6 4 6 5 6 6 8 7 2 8 2 9 3 10 0 11 2 12 1 13 0 14 0 15 0 16 1 Total

Here mean,

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

 Marks Frequency 2 1 3 6 4 6 5 6 6 8 7 2 8 2 9 3 10 0 11 2 12 1 13 0 14 0 15 0 16 1 Total

And we know standard deviation is

Substituting values from above table, we get

Hence the mean and standard deviation of the marks are and respectively.

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