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2.Mean, Median & Mode
Class 11 • Mathematics • NCERT
Mean, Median & Mode
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In this lesson, students learn how to calculate and interpret the mean, median, and mode of a data set as prescribed by NCERT Class 11 Statistics.
Lesson Objectives
- Calculate mean, median, and mode for ungrouped data.
- Understand when to use each measure.
- Apply correct steps in exam questions.
- Interpret results meaningfully.
1. Arithmetic Mean
The mean is obtained by dividing the sum of all observations by the total number of observations.
Mean = (Sum of observations) / n
Example:
Data: 4, 6, 10
Mean = (4 + 6 + 10) / 3 = 20 / 3
2. Median
The median is the middle value when data is arranged in ascending or descending order.
• Odd number of observations → middle value
• Even number → average of two middle values
• Even number → average of two middle values
Example:
Data: 2, 5, 7, 9, 12
Median = 7
3. Mode
The mode is the value that occurs most frequently in the data set.
A data set may have one mode, more than one mode, or no mode.
Example:
Data: 1, 3, 3, 5, 6
Mode = 3
4. Choosing the Right Measure
• Mean → sensitive to extreme values
• Median → best for skewed data
• Mode → most frequent observation
• Median → best for skewed data
• Mode → most frequent observation
5. Relationship Between Mean, Median & Mode
Mode = 3 Median − 2 Mean
Valid for moderately skewed distributions.
Practice Questions (NCERT)
- Find the mean of: 5, 7, 9.
- Find the median of: 3, 8, 5, 10, 12.
- Find the mode of: 2, 4, 4, 6, 7.
- Which measure is most affected by extreme values?
- Which measure is best for skewed data?
- Can a data set have no mode?
- State the formula connecting mean, median, and mode.
- Arrange data before finding median — True or False?
- Which measure shows the most common value?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- 7
- 8
- 4
- Mean
- Median
- Yes
- Mode = 3 Median − 2 Mean
- True
- Mode
- Yes
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