Summary
Chapter 13 Statistics covers measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, variance, and standard deviation) for both ungrouped and grouped data, enabling analysis of how data varies from a central value.
Statistics is the science of analyzing and interpreting data to understand variability. While measures of central tendency like mean and median show where data clusters, measures of dispersion reveal how scattered or bunched data are. Key dispersion measures include range (maximum − minimum), mean deviation (average absolute deviation from a central value), and standard deviation (square root of variance). These concepts apply to ungrouped data (individual observations), discrete frequency distributions, and continuous frequency distributions.
Key points & formulas
- 01Measures of central tendency alone are insufficient; dispersion measures reveal data scatter and variability
- 02Range is the simplest dispersion measure: difference between maximum and minimum values
- 03Mean deviation measures average absolute deviation from mean or median; cannot be algebraically manipulated
- 04Variance is the mean of squared deviations from the mean; standard deviation is its positive square root
- 05Step-deviation method simplifies calculations when data values or class midpoints are large
- 06Different dispersion measures apply: range for quick estimates, mean deviation for absolute deviations, standard deviation for algebraic analysis
Frequently asked questions
01What is the difference between mean deviation and standard deviation?
Mean deviation uses absolute values of deviations (ignoring signs), making it simple but not algebraically manipulative. Standard deviation uses squared deviations, allowing further mathematical treatment. Standard deviation is preferred in statistical studies because the sum of deviations from mean equals zero, making mean deviation about mean less scientific.
02Why are measures of dispersion needed when we already have measures of central tendency?
Measures of central tendency (mean, median) only show where data clusters. Two datasets with the same mean and median can have very different distributions—one may be tightly bunched while the other is highly scattered. Dispersion measures quantify this spread, providing complete information about data variability.
03How do you calculate standard deviation for grouped data?
For continuous frequency distributions, replace each class with its midpoint and apply the standard deviation formula: σ = √(1/N × Σfi(xi − x)²), where fi is frequency, xi is midpoint, N is total frequency, and x is the mean. The shortcut method uses step-deviations to simplify calculations: σ = h√(1/N × [NΣfiyi² − (Σfiyi)²]).
04Is the NCERT Class 11 Maths Chapter 13 PDF free to download?
Yes, the NCERT Class 11 Maths Chapter 13 textbook PDF is free to download.
More chapters in Mathematics
This is the complete Mathematics Chapter 13 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 11 textbooks.
Read offline with notes, solutions & mock tests
CBSE Prepmaster — free on iOS & Android