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:

Determine the Mean and Standard Deviation
Marks2345678910111213141516
Frequency166882230210001

Answer:

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

Table of the Given Data and Append Other Columns After Calculations
Marks Frequency
21
36
46
56
68
72
82
93
100
112
121
130
140
150
161
Total

Here mean,

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

The Above Table with More Columns
Marks Frequency
21
36
46
56
68
72
82
93
100
112
121
130
140
150
161
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.