Measures of Dispersion — Chapter Summary
Gujarat Board · Class 11 · Statistics
Summary of Measures of Dispersion for Gujarat Board Class 11 Statistics. Part of the Gujarat Board Class 11 Statistics syllabus.
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Overview
Measures of dispersion complement measures of central tendency by revealing how spread out or scattered data points are from the average value. While averages tell us about the central value, dispersion measures help us understand the variability within the data. This chapter explores various method
Key Concepts
A measure that shows how far
A measure that shows how far observations are scattered from the central value (mean, median, or mode). It indicates the degree of variability in a da
Absolute measures are expressed in
Absolute measures are expressed in the same units as the original data (like kg, cm, rupees). Relative measures are unit-free ratios or percentages th
The simplest measure of dispersion calculated
The simplest measure of dispersion calculated as the difference between the highest and lowest values in a dataset. Formula: R = xH - xL. Coefficient
A positional measure based on
A positional measure based on the middle 50% of data, calculated as Qd = (Q3 - Q1)/2. Also called semi-inter-quartile range. Coefficient = (Q3 - Q1)/(
The average of absolute deviations
The average of absolute deviations of all observations from the mean. Formula: MD = Σ|xi - x̄|/n for ungrouped data. Uses all observations and conside
Learning Objectives
- Understand the meaning and importance of dispersion in statistical analysis
- Distinguish between absolute and relative measures of dispersion
- Calculate and interpret Range and its coefficient
- Compute Quartile Deviation and its coefficient for positional analysis
- Master the calculation of Mean Deviation from ungrouped and grouped data
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