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Question:
Answered & Verified by Expert
$$
\text { Calculate variance of the following data: }
$$
$$
\begin{array}{|c|c|}
\hline \text { Class interval } & \text { Frequency } \\
\hline 4-8 & 3 \\
8-12 & 6 \\
12-16 & 4 \\
16-20 & 7 \\
\hline
\end{array}
$$
\text { Calculate variance of the following data: }
$$
$$
\begin{array}{|c|c|}
\hline \text { Class interval } & \text { Frequency } \\
\hline 4-8 & 3 \\
8-12 & 6 \\
12-16 & 4 \\
16-20 & 7 \\
\hline
\end{array}
$$
Solution:
2531 Upvotes
Verified Answer
$$
\begin{aligned}
&\text { Mean }(\overline{\mathrm{x}})=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}} \\
&=\frac{3 \times 6+6 \times 10+4 \times 14+7 \times 18}{20}=13
\end{aligned}
$$
Variance
$$
\begin{aligned}
\left(\sigma^2\right) &=\frac{\sum f_i\left(x_i-\bar{x}\right)^2}{\sum f_i} \\
&=\frac{3(-7)^2+6(-3)^2+4(1)^2+7(5)^2}{20} \\
&=\frac{147+54+4+175}{20}=19
\end{aligned}
$$
\begin{aligned}
&\text { Mean }(\overline{\mathrm{x}})=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}} \\
&=\frac{3 \times 6+6 \times 10+4 \times 14+7 \times 18}{20}=13
\end{aligned}
$$
Variance
$$
\begin{aligned}
\left(\sigma^2\right) &=\frac{\sum f_i\left(x_i-\bar{x}\right)^2}{\sum f_i} \\
&=\frac{3(-7)^2+6(-3)^2+4(1)^2+7(5)^2}{20} \\
&=\frac{147+54+4+175}{20}=19
\end{aligned}
$$
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