This document discusses various measures of dispersion used to describe the variability or spread of data beyond just the mean. It describes the range, interquartile range, and standard deviation as common measures of dispersion. The range is defined as the difference between the largest and smallest values. The interquartile range uses the first and third quartiles to indicate spread. Standard deviation uses the average squared deviations from the mean to quantify variability. Absolute measures express dispersion in the original units, while relative measures use ratios or percentages compared to the average. A good measure of dispersion should be easy to calculate, consider all observations, be clearly defined, and allow for further analysis.

1. MEASURES OF DISPERSION

2. MEANING
• Two data sets can have the same mean but they
can be entirely different. Thus to describe data,
one needs to know the extent of variability. This is
given by the measures of dispersion.

3. MEASURES OF MOD
• Range
• iinterquartile range
• Standard deviation are the three commonly used measures of
dispersion

4. RANGE
• It is the simplest method of measurement of dispersion and
defines the difference between the largest and the smallest
item in a given distribution.
• Formula:-Range = Y max – Y min

5. QUARTILE DEVIATIONS
• It is known as semi-interquartile range, i.e., half of the
difference between the upper quartile and lower quartile.
• The first quartile is derived as Q, the middle digit Q1 connects
the least number with the median of the data.
• FORMULA:- Q = ½ × (Q3 – Q1)

6. MEAN DEVIATION
• Mean deviation is the arithmetic mean (average) of deviations
of observations from a central value.
• Mean deviation can be evaluated by using the formula: A = 1⁄n
[∑i|xi – A|]

7. STANDARD DEVIATION
• Standard deviation is the square root of the arithmetic average
of the square of the deviations measured from the mean.
• Σ = [(Σi (yi – ȳ) ⁄ n] ½ = [(Σ I yi 2 ⁄ n) – ȳ 2] ½

8. TYPES OF MEASURES OF DISPERSION
• ABSOLUTE MEASURE
• Absolute measures of dispersion are expressed in the unit of
variable itself, like kilograms, rupees, centimeters, marks.
• RELATIVE MEASURE
• Relative measures of dispersion are obtained as ratios or
percentages of the average.

9. Characteristics of a Good Measure of
Dispersion
• It should be easy to calculate and simple to understand.
• It should be based on all the observations of the series.
• It should be rigidly defined.
• • It should be capable of further mathematical treatment and
statistical analysis.

10. • THESE ARE THE MAJOR TYPES AND MEASURES OF MEASURES
OF DISPERSION.