NCERT Class 11-Math՚S: Exemplar Chapter – 15 Statistics Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 19:

The weights of coffee in jars is shown in the following table:

Weights of Coffee in 70 Jars
Weight

(in grams)

Frequency
200 - 20113
201 - 20227
202 - 20318
203 - 20410
204 - 2051
205 - 2061

Determine variance and standard deviation of the above distribution.

Answer:

Given: the weights of coffee in 70 jars

To find: the variance and standard deviation of the distribution

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

The Weights of Coffee in 70 Jars
Weight (in grams)Mid Value Frequency
Total

Here mean,

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

The Above Table with More Columns
Weight (in grams)Mid Value Frequency
Total

And we know standard deviation is

Substituting values from above table, we get

And

Hence the variance and standard deviation of the distribution are 1.166g and 1.08 respectively.