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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.  

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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,
\[\sigma\] = \[\sqrt{\text{ Variance} } = \sqrt{1 . 162} = 1 . 08 \text{ gm }\]
 

 

  Is there an error in this question or solution?
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APPEARS IN

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