Mean of Grouped Data | Statistics | Class 10

01 · CLASS MARK

Class Mark (xᵢ)

For grouped data, the central representative value of each class interval is called the class mark (xᵢ):

Class Mark xᵢ = (Upper Class Limit + Lower Class Limit) / 2

02 · THREE METHODS

Formulas for Finding Mean (x̄)

1. Direct Method

Direct Method

x̄ = Σfᵢxᵢ / Σfᵢ (Best when values of fᵢ and xᵢ are small).

2. Assumed Mean

Assumed Mean Method

x̄ = a + (Σfᵢdᵢ / Σfᵢ) where dᵢ = xᵢ - a (a is assumed mean).

3. Step-Deviation

Step-Deviation Method

x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h where uᵢ = (xᵢ - a)/h and h is class size.

03 · SOLVED NCERT EXAMPLE

Step-by-Step Problem Solving

EXAMPLE 1

Find the mean marks obtained by 30 students in a mathematics test

Given distribution table:

Class Interval | Frequency fᵢ | Class Mark xᵢ | fᵢxᵢ
10 - 25         | 2             | 17.5          | 35.0
25 - 40         | 3             | 32.5          | 97.5
40 - 55         | 7             | 47.5          | 332.5
55 - 70         | 6             | 62.5          | 375.0
70 - 85         | 6             | 77.5          | 465.0
85 - 100        | 6             | 92.5          | 555.0
-------------------------------------------------------------
Total           | Σfᵢ = 30     | -            | Σfᵢxᵢ = 1860.0

Calculating Mean by Direct Method:

x̄ = Σfᵢxᵢ / Σfᵢ = 1860 / 30 = 62.0

Mean marks obtained by students is 62.

04 · QUICK SUMMARY

Key Takeaways

Class mark xᵢ = (Upper Limit + Lower Limit) / 2.

Direct method formula: x̄ = Σfᵢxᵢ / Σfᵢ.

Assumed mean method reduces big numbers by using dᵢ = xᵢ - a.