Question

Find the mean of the following data by short-cut method.
CI
40-45
45-50
50-55
55-60
60-65
65-70
70-75
75-80

F
5
12
20
15
10
8
5
4

Answer 1

hope my answer helps you.

Answer 2

➡️Solution:

Short method,we can say it as Direct Mean Method,but some times it has complex calculations

$\begin{table}[] \begin{tabular}{|l|l|l|l|} \cline{1-4} \begin{tabular}[c]{@{}l@{}}Class\\ Interval\end{tabular} & Frequency & \begin{tabular}[c]{@{}l@{}}Class \\ Mark (x_{i})\end{tabular} & x_{i}f_{i} \\ \cline{1-4} 40-45 & 5 & 42.5 & 212.5 \\ \cline{1-4} 45-50 & 12 & 47.5 & 570 \\ \cline{1-4} 50-55 & 20 & 52.5 & 1050 \\ \cline{1-4} 55-60 & 15 & 57.5 & 862.5 \\ \cline{1-4} 60-65 & 10 & 62.5 & 625 \\ \cline{1-4} 65-70 & 8 & 67.5 & 540 \\ \cline{1-4} 70-75 & 5 & 72.5 & 362.5 \\ \cline{1-4} 75-80 & 4 & 77.5 & 310 \\ \cline{1-4} Total & 79 & & 4532.5 \\ \cline{1-4} \end{tabular} \end{table}$

Direct mean Method:

$\bar x = \frac{\Sigma x_{i}f_{i}}{\Sigma f_{i}} \\ \\ \bar x= \frac{4532.5}{79} \\ \\ \bar x= 57.37$

Hope it helps you