MEASUREMENT OF DISPERSION

Measures of dispersion are statistical tools used to show how spread out or scattered a set of data is around a central value (mean, median, or mode). Measures of dispersion tells us how reliable or varied that value is.

Importance of Dispersion

  1. Shows the variability of data
  2. Helps determine the consistency of performance
  3. Enables comparison between groups
  4. Assists in decision-making and evaluation
  5. Indicates reliability of the mean

Types of Measures of Dispersion

1. Range

The simplest measure of dispersion.

Formula: Highest number - Lowest number 

Example:

(It'll be done in class)

Advantages

  1. Easy to calculate
  2. Quick estimate of spread

Disadvantages 

  1. Uses only two values
  2. Not very reliable

2. Quartile Deviation (Semi-Interquartile Range)

It measures the spread of the middle 50% of data.

Formula: Q3-Q1/2

Where:

Q1 = First quartile

Q3 = Third quartile

Advantages 

  1. Not affected by extreme values
  2. More reliable than range

Disadvantage

1. Ignores half of the data


3. Mean Deviation (Average Deviation)

It is the average of the absolute deviations from the mean or median.


Advantages 

1. Uses all data

2. Simple to understand

Disadvantages

1. Ignores signs (+/−)

2. Less commonly used.


4. Variance

Variance measures the average squared deviation from the mean


Merits:

Uses all observations

Important in advanced statistics

Demerits:

Units are squared (less intuitive)

5. Standard Deviation

The most widely used measure of dispersion. It is the square root of variance.

Merits:

Highly reliable

Uses all data

Widely accepted

Demerits:

Slightly complex to calculate

Application in Physical and Health Education (PHE)

Determines consistency in performance (e.g., running times)

Compares fitness levels between students

Evaluates effectiveness of training programmes

Helps identify irregular or extreme performances


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