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, ……, m_n and the frequencies of the corresponding classes be f₁, f₂, f₃, f₄, …….., f_n 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.

Solution:

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

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.

Solution:

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

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

                                  = $\frac{2811.5}{73}$

                                  = 38.51 (Approx.).

9th Grade Math

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