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A random sample of 20 people is classified in the followin, 1
\begin{array}{|c|c|}
\hline Age & Frequency \\
\hline 15-25 & 2 \\
\hline 25-35 & 4 \\
\hline 35-45 & 6 \\
\hline 45-55 & 5 \\
\hline 55-65 & 3 \\
\hline
\end{array} the mean age of this group of people?
Options:
\begin{array}{|c|c|}
\hline Age & Frequency \\
\hline 15-25 & 2 \\
\hline 25-35 & 4 \\
\hline 35-45 & 6 \\
\hline 45-55 & 5 \\
\hline 55-65 & 3 \\
\hline
\end{array} the mean age of this group of people?
Solution:
2511 Upvotes
Verified Answer
The correct answer is:
415
\begin{array}{|c|c|c|c|}
\hline Age & Mid value \mathbf{x}_{\mathbf{i}} & Frequency \mathbf{f}_{\mathbf{i}} & \mathbf{f}_{\mathbf{i}} \mathbf{x}_{\mathbf{i}} \\
\hline 15-25 & 20 & 2 & 40 \\
\hline 25-35 & 30 & 4 & 120 \\
\hline 35-45 & 40 & 6 & 240 \\
\hline 45-55 & 50 & 5 & 250 \\
\hline 55-65 & 60 & 3 & 180 \\
\hline & & \mathbf{\Sigma} \mathbf{f}_{\mathrm{i}}=20 & \mathbf{\Sigma x}_{\mathbf{i}} \mathbf{f}_{\mathbf{i}}=830 \\
\hline
\end{array}
$\Rightarrow$ Mean age $=\frac{\Sigma x_{i} f_{i}}{\Sigma f_{i}}=\frac{830}{20}=41.5$
\hline Age & Mid value \mathbf{x}_{\mathbf{i}} & Frequency \mathbf{f}_{\mathbf{i}} & \mathbf{f}_{\mathbf{i}} \mathbf{x}_{\mathbf{i}} \\
\hline 15-25 & 20 & 2 & 40 \\
\hline 25-35 & 30 & 4 & 120 \\
\hline 35-45 & 40 & 6 & 240 \\
\hline 45-55 & 50 & 5 & 250 \\
\hline 55-65 & 60 & 3 & 180 \\
\hline & & \mathbf{\Sigma} \mathbf{f}_{\mathrm{i}}=20 & \mathbf{\Sigma x}_{\mathbf{i}} \mathbf{f}_{\mathbf{i}}=830 \\
\hline
\end{array}
$\Rightarrow$ Mean age $=\frac{\Sigma x_{i} f_{i}}{\Sigma f_{i}}=\frac{830}{20}=41.5$
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