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The weights of coffee in 70 jars is shown in the following table:
$$
\begin{array}{|c|c|}
\hline \text { Weight (in grams) } & \text { Frequency } \\
\hline 200-201 & 13 \\
201-202 & 27 \\
202-203 & 18 \\
203-204 & 10 \\
204-205 & 1 \\
205-206 & 1 \\
\hline
\end{array}
$$
Determine variance and standard deviation of the above distribution.
$$
\begin{array}{|c|c|}
\hline \text { Weight (in grams) } & \text { Frequency } \\
\hline 200-201 & 13 \\
201-202 & 27 \\
202-203 & 18 \\
203-204 & 10 \\
204-205 & 1 \\
205-206 & 1 \\
\hline
\end{array}
$$
Determine variance and standard deviation of the above distribution.
Solution:
1267 Upvotes
Verified Answer
$$
\begin{array}{|c|c|l|c|l|l|}
\hline \text { Class } & \boldsymbol{x} & \boldsymbol{f} & \boldsymbol{d}=\boldsymbol{x}-\mathbf{2 0 2 . 5} & \boldsymbol{f d} & \boldsymbol{f d}^2 \\
\hline 200-201 & 200.5 & 13 & -2 & -26 & 52 \\
201-202 & 201.5 & 27 & -1 & -27 & 27 \\
202-203 & 202.5 & 18 & 0 & 0 & 0 \\
203-204 & 203.5 & 10 & 1 & 10 & 10 \\
204-205 & 204.5 & 1 & 2 & 2 & 4 \\
205-206 & 205.5 & 1 & 3 & 3 & 9 \\
\hline & & 70 & & -38 & 102 \\
\hline
\end{array}
$$
Let $A=$ Assumed Mean $=202.5$
$$
\Rightarrow \text { S.D. }=\sqrt{\frac{102}{70}-\left(\frac{-38}{70}\right)^2}
$$
$$
=\sqrt{1.162}=1.08 \mathrm{gm}
$$
$\&$ variance $=(\mathrm{SD})^2=1.162 \mathrm{gm}$
\begin{array}{|c|c|l|c|l|l|}
\hline \text { Class } & \boldsymbol{x} & \boldsymbol{f} & \boldsymbol{d}=\boldsymbol{x}-\mathbf{2 0 2 . 5} & \boldsymbol{f d} & \boldsymbol{f d}^2 \\
\hline 200-201 & 200.5 & 13 & -2 & -26 & 52 \\
201-202 & 201.5 & 27 & -1 & -27 & 27 \\
202-203 & 202.5 & 18 & 0 & 0 & 0 \\
203-204 & 203.5 & 10 & 1 & 10 & 10 \\
204-205 & 204.5 & 1 & 2 & 2 & 4 \\
205-206 & 205.5 & 1 & 3 & 3 & 9 \\
\hline & & 70 & & -38 & 102 \\
\hline
\end{array}
$$
Let $A=$ Assumed Mean $=202.5$
$$
\Rightarrow \text { S.D. }=\sqrt{\frac{102}{70}-\left(\frac{-38}{70}\right)^2}
$$
$$
=\sqrt{1.162}=1.08 \mathrm{gm}
$$
$\&$ variance $=(\mathrm{SD})^2=1.162 \mathrm{gm}$
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