Class 11 Maths Chapter 13 Statistics – Revision Notes

Two data sets can share the same mean and still look very different, which is why Chapter 13 of Class 11 Maths introduces measures of dispersion. Range, mean deviation, variance, and standard deviation each describe spread in their own way, with standard deviation the most commonly used.

Last Updated: September 23, 2026

Reference figure: a histogram of grouped data, illustrating how frequency-distribution data used throughout this chapter is visualised.

Measures of Dispersion

• Range = max−min.
• Mean deviation = ∑|xi−mean|/n.
• Variance σ² = ∑(xi−mean)²/n.
• Standard deviation σ = √(variance).

Key Points

• Std dev always ≥ 0; 0 means all values identical.
• Smaller std dev = more consistent/less spread data.
• Std dev preferred over variance (same units as data).

One-Line Summary

Measures of dispersion (range, mean deviation, variance, standard deviation) describe how spread out data is around the mean, with standard deviation being the most widely used since it returns to the data’s original units.

Frequently Asked Questions

Why do we need measures of dispersion in addition to measures of central tendency like mean?
Two data sets can have the same mean but very different spreads. Measures of dispersion such as range, mean deviation, variance and standard deviation describe how much the data varies around the mean, giving a fuller picture.

What does a smaller standard deviation indicate about a data set?
A smaller standard deviation means the data points are clustered closer to the mean, indicating more consistency, while a larger standard deviation means the data is more spread out.

Written by Satish

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