Chapter 13 — Statistics

Chapter 13 of the Class 11 Maths NCERT textbook, "Statistics", covers measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, variance, standard deviation) for grouped and ungrouped data, analysing how data varies from a central value.

• Why central tendency isn't enough — The chapter's key insight is that knowing where data clusters says nothing about how spread out it is, so dispersion measures are introduced to reveal the scatter that averages alone hide.
• A ladder of dispersion measures — It moves from the simple range through mean deviation to variance and standard deviation, each capturing spread more finely, and explains which measure suits quick estimates versus algebraic analysis.
• Working across data formats — These measures are applied to ungrouped observations and to discrete and continuous frequency distributions, with the step-deviation method simplifying calculation when values or class midpoints are large.

1. 01Measures of central tendency alone are insufficient; dispersion measures reveal data scatter and variability
2. 02Range is the simplest dispersion measure: difference between maximum and minimum values
3. 03Mean deviation measures average absolute deviation from mean or median; cannot be algebraically manipulated
4. 04Variance is the mean of squared deviations from the mean; standard deviation is its positive square root
5. 05Step-deviation method simplifies calculations when data values or class midpoints are large
6. 06Different dispersion measures apply: range for quick estimates, mean deviation for absolute deviations, standard deviation for algebraic analysis