Measures Of Dispersion
Telangana Open School (TOSS) · Class 12 · Mathematics
Summary of Measures Of Dispersion for Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, important points, and chapter overview.
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Overview
In statistics, knowing the average (mean, median, mode) of a data set is not enough to fully understand it. Two data sets can have the same average but differ greatly in how spread out the values are. This spread or variability is measured using 'Measures of Dispersion'. This chapter introduces key
Key Concepts
The range is the simplest measure
The range is the simplest measure of dispersion. It is calculated as the difference between the highest and lowest values in a data set. For example,
Mean deviation is the average
Mean deviation is the average of the absolute differences between each data point and the mean (or median). For ungrouped data, it is calculated as th
Variance is the average of
Variance is the average of the squared differences from the mean. For ungrouped data, it is the sum of squared deviations divided by the number of obs
Standard deviation is the positive square
Standard deviation is the positive square root of the variance. It is denoted by σ (sigma) and is expressed in the same units as the original data, ma
Learning Objectives
- Explain the purpose of measures of dispersion
- Compute range, mean deviation, variance, and standard deviation for ungrouped and grouped data
- Calculate mean deviation from mean and median
- Understand and apply variance and standard deviation formulas
- Use step deviation method for easier calculations
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