Question

Calculate the mean of the following data :

Class :	4 – 6	7 – 9	10 – 12	13 – 15
Frequency :	5	4	9	10

Answer 1

Step 1: Find the class midpoints
The midpoints ($x_i$) are calculated as the average of the lower and upper limits of each class:
\[x_1 = \frac{4 + 6}{2} = 5, \quad x_2 = \frac{7 + 9}{2} = 8, \quad x_3 = \frac{10 + 12}{2} = 11, \quad x_4 = \frac{13 + 15}{2} = 14.\]
Step 2: Multiply midpoints by frequencies
Construct the table as follows:
\[\begin{array}{|c|c|c|c|}\hline\text{Class} & \text{Frequency } (f_i) & \text{Midpoint } (x_i) & f_i x_i \\\hline4 - 6 & 5 & 5 & 25 \\7 - 9 & 4 & 8 & 32 \\10 - 12 & 9 & 11 & 99 \\13 - 15 & 10 & 14 & 140 \\\hline\end{array}\]
Step 3: Calculate the total frequency and total $f_i x_i$ 
\[\sum f_i = 5 + 4 + 9 + 10 = 28.\]
\[\sum f_i x_i = 25 + 32 + 99 + 140 = 296.\]
Step 4: Calculate the mean
The formula for the mean is:
\[\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}.\]
Substitute the values:
\[\text{Mean} = \frac{296}{28} = 10.57.\]
Correct Answer: Mean = 10.57