# The Weight of Coffee in 70 Jars is Shown in the Following Table: - Mathematics

The weight of coffee in 70 jars is shown in the following table:

 Weight (in grams): 200–201 201–202 202–203 203–204 204–205 205–206 Frequency: 13 27 18 10 1 1

Determine the variance and standard deviation of the above distribution.

#### Solution

 Weight (in grams) Mid-Values $\left( x_i \right)$ Frequency $\left( f_i \right)$ $d_i = x_i - 202 . 5$ $d_i^2$ $f_i d_i$ $f_i d_i^2$ 200–201 200.5 13 −2 4 −26 52 201–202 201.5 27 −1 1 −27 27 202–203 202.5 18 0 0 0 0 203–204 203.5 10 1 1 10 10 204–205 204.5 1 2 4 2 4 205–206 205.5 1 3 9 3 9 N = $\sum_{} f_i = 70$ $\sum_{} f_i d_i = - 38$ $\sum_{}f_i d_i^2 = 102$

Now,

Variance,

$\sigma^2$
$= \left( \frac{1}{N} \sum_{} f_i d_i^2 \right) - \left( \frac{1}{N} \sum_{} f_i d_i \right)^2$
$= \left( \frac{1}{70} \times 102 \right) - \left( \frac{1}{70} \times \left( - 38 \right) \right)^2$
$= 1 . 457 - 0 . 295$
$= 1 . 162 gm$
Standard deviation,
$\sigma$ = $\sqrt{\text{ Variance} } = \sqrt{1 . 162} = 1 . 08 \text{ gm }$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.6 | Q 7 | Page 42