# Mean of Classified Data

Here we will learn how to find the mean of classified data (continuous and discontinuous).

If the class marks of the class intervals be m1, m2, m3, m4, ……, mn and the frequencies of the corresponding classes be f1, f2, f3, f4, …….., fn then the mean of the distribution is given by

Mean = A or ($$\overline{x}$$) = $$\frac{m_{1}f_{1} + m_{2}f_{2} + m_{3}f_{3} + m_{4}f_{4} + .... + m_{n}f_{n}}{f_{1} + f_{2} + f_{3} + f_{4} + .... + f_{n}}$$

Symbolically, A = $$\frac{\sum m_{i}f_{i}}{\sum f_{i}}$$

This is the direct method of finding the mean of classified data.

Solved Examples on Mean of Classified Data (Continuous and Discontinuous)

1. Find the mean of the following frequency distribution.

Class Interval

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

Frequency

4

11

8

7

10

5

Solution:

Here, the calculations are done in the table given below.

 Class Interval Class Mark (mi) Frequency (fi) mifi 0 - 10 5 4 20 10 - 20 15 11 165 20 - 30 25 8 200 30 - 40 35 7 245 40 - 50 45 10 450 50 - 60 55 5 275 $$\sum f_{i}$$ = 45 $$\sum m_{i}f_{i}$$ = 1355

Therefore, mean A = $$\frac{\sum m_{i}f_{i}}{\sum f_{i}}$$

= $$\frac{1355}{45}$$

= 30$$\frac{1}{9}$$

2. Find the mean of the following frequency distribution.

Class Interval

11 - 20

21 - 30

31 - 40

41 - 50

51 - 60

Frequency

12

10

15

16

20

Solution:

After making the class intervals overlapping, we do the following calculations.

 Class Interval Class Mark (mi) Frequency (fi) mifi 10.5 - 20.5 15.5 12 186.0 20.5 - 30.5 25.5 10 255.0 30.5 - 40.5 35.5 15 532.5 40.5 - 50.5 45.5 16 728.0 50.5 - 60.5 55.5 20 1110.0 $$\sum f_{i}$$ = 73 $$\sum m_{i}f_{i}$$ = 2811.5

Therefore, mean A = $$\frac{\sum m_{i}f_{i}}{\sum f_{i}}$$

= $$\frac{2811.5}{73}$$

= 38.51 (Approx.).

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Formation of Greatest and Smallest Numbers | Arranging the Numbers

May 19, 24 03:36 PM

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

2. ### Formation of Numbers with the Given Digits |Making Numbers with Digits

May 19, 24 03:19 PM

In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

3. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

May 19, 24 02:23 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

4. ### Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

May 19, 24 01:26 PM

Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…