Measures of Central Tendency | Class 11 Economics Notes

How Arithmetic Mean is Calculated

The arithmetic mean can be calculated using different methods depending on the nature and size of the data set:

1. Arithmetic Mean for Ungrouped Data:

• Direct Method: Sum all observations and divide by the number of observations.
• Assumed Mean Method: Used when data size is large or numbers are big. An assumed mean (A) is selected, deviations (d = X - A) are calculated, summed, and then the actual mean is found by adding A to the average deviation.
• Step Deviation Method: Simplifies calculations by dividing deviations by a common factor (c) to reduce large numbers. The formula becomes X̄ = A + (Σd')/N × c, where d' = d/c.

2. Arithmetic Mean for Grouped Data:

• Discrete Series: Multiply each value by its frequency, sum these products, and divide by total frequency.
• Continuous Series: Use mid-points of class intervals as values, multiply by frequencies, sum, and divide by total frequency.

Example 1 (Direct Method for Ungrouped Data): Calculate mean marks of students scoring 40, 50, 55, 78, 58.

X̄ = (40 + 50 + 55 + 78 + 58) / 5 = 56.2

Example 2 (Assumed Mean Method): Weekly incomes of 10 families are given. Assuming mean A = 850, deviations d = X - 850 are calculated, summed, and mean computed as:

X̄ = A + (Σd)/N = 850 + 2660/10 = Rs 1,116

Step Deviation Method further simplifies this by dividing deviations by 10.

These methods help in efficient and accurate calculation of arithmetic mean, especially for large or grouped data.

📊 Diagram: See figure_2: Reprint 2026-27 showing assumed mean method calculation; See table_1: Computation of Arithmetic Mean by Assumed Mean Method.

🔗 Connection: Leads to detailed calculation of arithmetic mean for grouped data.

Table on page 4 (13×4)