Measures of Central Tendency | Class 11 Economics Notes

Calculation of arithmetic mean for Grouped data

Grouped data is data presented in classes or categories with corresponding frequencies. The arithmetic mean for grouped data is calculated differently based on whether the data is discrete or continuous.

1. Discrete Series:

• Direct Method: Multiply each observation (X) by its frequency (f), sum all products (ΣfX), and divide by total frequency (Σf).
• Assumed Mean Method: Select an assumed mean (A), calculate deviations d = X - A, multiply by frequency to get fd, sum (Σfd), then compute mean as X̄ = A + (Σfd) / (Σf).
• Step Deviation Method: Simplify by dividing deviations by a common factor c, calculate d' = d / c, multiply by frequency to get fd', sum (Σfd'), and mean is X̄ = A + (Σfd') / (Σf) × c.

Example 3 (Direct Method for Discrete Series): Plot sizes in a colony are 100, 200, and 300 sq. meters with frequencies 200, 50, and 10 respectively.

Calculate mean plot size:

X̄ = ΣfX / Σf = (200×100 + 50×200 + 10×300) / (200 + 50 + 10) = 33000 / 260 = 126.92 sq. meters

2. Continuous Series:

• Use mid-points of class intervals as values.
• Multiply mid-points by frequencies, sum, and divide by total frequency.
• Assumed mean and step deviation methods apply similarly.

Example 4 demonstrates calculation of average marks using direct and step deviation methods for continuous data with class intervals and frequencies.

These methods allow efficient calculation of mean for large data sets presented in grouped form, facilitating summarisation and analysis.

📊 Diagram: See table_2: Computation of Arithmetic Mean by Direct Method; See table_3: Computation of Average Marks for Exclusive Class Interval by Direct Method.

🧪 Activity: Find the mean plot size for the data given in example 3, by using step deviation and assumed mean methods.

🔗 Connection: Prepares for understanding Median as another measure of central tendency.

Table on page 5 (6×5)

Table on page 6 (11×6)