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1.Measures of Central Tendency
Class 11 • Mathematics • NCERT
Measures of Central Tendency
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This lesson introduces measures of central tendency as prescribed by NCERT Class 11 Statistics. Students learn how to represent data using mean, median, and mode to understand typical values.
Lesson Objectives
- Understand the concept of central tendency.
- Calculate mean, median, and mode.
- Apply formulas to simple data sets.
- Interpret results meaningfully.
1. What Is Central Tendency?
A measure of central tendency is a single value that represents the centre or typical value of a data set.
It helps us summarise large data in a simple form.
2. Arithmetic Mean
The arithmetic mean is the sum of all observations divided by the number of observations.
Mean = (Sum of observations) / (Number of observations)
Example:
Data: 2, 4, 6, 8
Mean = (2 + 4 + 6 + 8) / 4 = 5
3. Median
The median is the middle value of a data set when observations are arranged in ascending or descending order.
If number of observations is odd → middle value
If even → average of two middle values
If even → average of two middle values
Example:
Data: 3, 5, 7, 9, 11
Median = 7
4. Mode
The mode is the value that occurs most frequently in a data set.
A data set may have one mode, more than one mode, or no mode.
Example:
Data: 2, 3, 3, 5, 7
Mode = 3
5. Relationship Between Mean, Median, and Mode
Mode = 3 Median − 2 Mean
This relation holds for moderately skewed distributions.
Practice Questions (NCERT)
- Define central tendency.
- Find the mean of: 4, 6, 8, 10.
- Find the median of: 3, 7, 5, 9, 11.
- Find the mode of: 2, 4, 4, 6, 8.
- Which measure is affected most by extreme values?
- State the formula connecting mean, median, and mode.
- Can a data set have more than one mode?
- Arrange data before finding median — True or False?
- Which measure represents the most frequent value?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- A single value representing centre of data
- 7
- 7
- 4
- Mean
- Mode = 3 Median − 2 Mean
- Yes
- True
- Mode
- Yes
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