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

Concept: For grouped data, the arithmetic mean is calculated using class midpoints. \[ \bar{x} = \frac{\sum f x}{\sum f} \] where, 
\( f \) = frequency 
\( x \) = class midpoint 
Step 1: Find Class Midpoints Midpoint formula: \[ x = \frac{\text{Lower limit + Upper limit}}{2} \] 

Step 2: Compute Totals \[ \sum f = 5 + 8 + 15 + 10 + 2 = 40 \] \[ \sum fx = 25 + 120 + 375 + 350 + 90 = 960 \] Step 3: Calculate Arithmetic Mean \[ \bar{x} = \frac{\sum fx}{\sum f} = \frac{960}{40} = 24 \] \[ \boxed{\bar{x} = 24} \]