Measures of Central Tendency | Class 11 Economics Notes

3. MEDIAN

Median is a positional measure of central tendency that divides a data set into two equal halves such that half the observations are less than or equal to the median and half are greater than or equal to it. It represents the middle value when data is arranged in ascending or descending order.

Median is less affected by extreme values (outliers) compared to arithmetic mean, making it a better measure when data contains such extremes.

To compute median:

• Arrange data in order.
• If the number of observations (N) is odd, median is the middle value.
• If N is even, median is the average of the two middle values.

Example 5: Data: 5, 7, 6, 1, 8, 10, 12, 4, 3 Sorted: 1, 3, 4, 5, 6, 7, 8, 10, 12 Median is the 5th value = 6

Position of median is given by (N + 1)/2-th item.

For grouped data:

• Discrete Series: Use cumulative frequency to locate median position.
• Continuous Series: Identify median class where N/2-th item lies and use formula:

Median = L + [(N/2 - cf) / f] × h

Where L = lower limit of median class, cf = cumulative frequency before median class, f = frequency of median class, h = class width.

Example 7 and 8 illustrate median calculation for discrete and continuous series respectively.

Median is a robust measure, focusing on central data points and less influenced by outliers.

📊 Diagram: See table_4: Mean and Median of different series; See table_5 and figure_3: Computation of Median for Discrete Series; See table_6 and figure_4: Computation of Median for Continuous Series.

🧪 Activity: Find mean and median for different series and observe the effect of extreme values; Discuss if median is better than mean.

🔗 Connection: Leads to the study of Quartiles and Percentiles as further positional measures.

Table on page 8 (5×4)

Table on page 8 (2×5)

Table on page 9 (5×3)