Question

Calculate the Arithmetic Mean for the following data set: Class Interval: 0–10, 10–20, 20–30, 30–40, 40–50 Frequency: 5, 8, 15, 10, 2

Hint:

For grouped data, always use class midpoints instead of class limits when calculating the mean.

Answer 1

To calculate the Arithmetic Mean of grouped data, we use the formula:

Mean (x̄) = Σ(fx) / Σf

Where:
f = frequency
x = class mark (midpoint of class interval)

Step 1: Find the Class Marks (Midpoints)
Class Interval → Class Mark (x)
0–10 → (0 + 10)/2 = 5
10–20 → 15
20–30 → 25
30–40 → 35
40–50 → 45

Step 2: Calculate fx

Class Interval | f | x | fx
0–10 | 5 | 5 | 25
10–20 | 8 | 15 | 120
20–30 | 15 | 25 | 375
30–40 | 10 | 35 | 350
40–50 | 2 | 45 | 90

Σf = 5 + 8 + 15 + 10 + 2 = 40
Σfx = 25 + 120 + 375 + 350 + 90 = 960

Step 3: Apply Formula
Mean = Σfx / Σf
Mean = 960 / 40
Mean = 24

Final Answer:
The Arithmetic Mean of the given data set is 24.