Median and Mode Class 11 Statistics, Measures of Central Tendency Explained

In statistics, Median and Mode Class 11 help identify the middle value and the most frequent value in a data set. These are important measures of central tendency Class 11 taught in statistics. Students also get Class 11 statistics chapter notes that explain Median Class 11 explanation and Mode Class 11 statistics in detail. They learn how to calculate median Class 11 and how to find mode Class 11 using appropriate formulas.

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Median

The median is the middle value of a data set when arranged in ascending or descending order.

• If the number of observations (n) is odd, the median is the value at the middle position.
  
  

• If n is even, the median is the average of the two middle values.

How to Calculate Median?

(A) For Ungrouped Data

1. Arrange data in ascending order.
   
   

2. Apply the formula:
   
   

Median and mode formulas for ungrouped data:

• If n is odd:
  Median = (n + 1) / 2 th term
  
  

• If n is even:
  Median = ( (n/2)th term + ( (n/2) + 1 )th term ) / 2
  
  

(B) For Grouped (Continuous) Data

Median = l1 + ((n/2 - cf) / f) × i

Where:

• l1 = lower limit of the median class
  
  

• cf = cumulative frequency before the median class
  
  

• f = frequency of the median class
  
  

• i = class width

Example (Ungrouped Data)

Question: Find the median of 10, 12, 14, 16, 18
Solution:
Arranged data: 10, 12, 14, 16, 18
n = 5 (odd)
Median = (5 + 1)/2 th term = 3rd term = 14

Mode

The mode is the value that appears most frequently in a data set. A data set may have no mode, one mode, or multiple modes. This is explained in Mode Class 11 statistics and highlighted in the Class 11 statistics chapter notes.

How to Calculate Mode?

(A) For Ungrouped Data

Count the frequency of each value and identify the one with the highest frequency.

(B) For Grouped (Continuous) Data

Mode = l1 + ((f1 - f0) / (2*f1 - f0 - f2)) × i

Where:

• l1 = lower limit of modal class

• f1 = frequency of modal class

• f0 = frequency of class preceding modal class

• f2 = frequency of class succeeding modal class

• i = class width

Example (Ungrouped Data)

Question: Find the mode of the data: 2, 4, 6, 10, 10, 14
Solution:
10 appears twice, more than any other value.
Mode = 10

Median and Mode Discrete and Continuous Series

Median and mode use different formulas for each type but follow the same concept of measures of central tendency Class 11.

• Discrete Series: Data given as separate values (e.g., 1, 2, 3…).

• Continuous Series: Data given in intervals (e.g., 0–10, 10–20…).

Median and Mode Formulas Summary

Below are key Median and mode formulas for quick reference:

Median and Mode Merits and Demerits

Median and Mode Class 11 are essential measures of central tendency Class 11. The table below highlights their key features: