Class Interval Arithmetic Mean Calculator

What is Class Interval Arithmetic Mean?

The class interval arithmetic mean is a measure of central tendency used for grouped data. It provides an estimate of the average value when data is presented in intervals or classes, each with an associated frequency.

Formula and Its Meaning

The formula for the class interval arithmetic mean is:

\[\bar{x} = \frac{\sum fx}{\sum f}\]

Where:

• \(\bar{x}\) is the arithmetic mean
• \(f\) is the frequency of each class
• \(x\) is the midpoint of each class interval
• \(\sum fx\) is the sum of the products of frequency and midpoint
• \(\sum f\) is the total frequency

Calculation Steps

1. Identify the midpoint of each class interval.
2. Multiply each midpoint by its corresponding frequency.
3. Sum up all these products (\(\sum fx\)).
4. Sum up all the frequencies (\(\sum f\)).
5. Divide the sum of products by the total frequency.

Example Calculation

Let's calculate the class interval arithmetic mean for the following data:

Class Interval	Frequency (f)	Midpoint (x)	fx
1-10	5	5.5	27.5
11-20	20	15.5	310
21-30	40	25.5	1020
31-40	80	35.5	2840
41-50	100	45.5	4550
Total	\(\sum f = 245\)		\(\sum fx = 8747.5\)

Applying the formula:

\[\bar{x} = \frac{\sum fx}{\sum f} = \frac{8747.5}{245} = 35.70\]

Therefore, the class interval arithmetic mean is 35.70.

Visual Representation

This histogram represents the frequency distribution of the class intervals. The red dashed line indicates the calculated arithmetic mean (35.70).