Statistics, measures of dispersion

1. MEASURES OF DISPERSION
•If everything were the same, we would have no need of
statistics. But, people's heights, ages, etc., do vary.
•We often need to measure the extent to
which scores in a dataset differ from each
other. Such a measure is called the dispersion
of a distribution.

2. • To know the average variation of
different values from the average of a
series
• To know the range of values
• To compare between two or more
series expressed in different units
• To know whether the Central Tendency
truly represent the series or not

3. TYPES OF MEASURES OF DISPERSION
MEASUR
ES OF
DISPERSI
ON
Range
(R)
Mean
Deviation
(MD)
Varianc
e
Standard
Deviation
(SD)

4. RANGE
The range is the difference between
the highest and lowest values of a
dataset.
Example : For the dataset {4, 6, 9, 3, 7}
the lowest value is 3, highest is 9, so
the range is 9-3=6.

5. MEAN
DEVIATION
• The mean deviation is the mean of the
absolute deviations ofa set of data
about the mean. For a sample size N,
the mean deviation is defined by

6. EXAMPLE :
five exams in a class and had scores of 92, 75, 95, 90, and 98.
Find the mean deviation for test scores.
We can say that on the average, test scores deviated by 6 points from the mean.

7. Varianc
e
The variance (σ2) is a measure of how far
each value in the data set is from the
mean.

8. Standard
Deviation
Standard Deviation it is the square root of
the Variance defined as

9. Example: took ten exams in STA 240 and had scores of
44, 50, 38, 96, 42, 47, 40,
39, 46, and 50. Find the variance for his test scores.
Mean = (44 + 50 +38 +96 + 42 +47 +40+ 39 + 46+ 50) /
10 = 49.2

10. COEFFICIENT OF
VARIATION
CV should be computed only for data measured on
a ratio scale. It may not have any
meaning for data on an interval scale.
The coefficient of variation (CV) is defined
as the ratio of the standard deviation to
the mean :
Cv = Standard Deviation / Mean

11. WhyCoefficient of V
ariation
The coefficient of variation (CV) is used
to compare different sets of data having
the units of measurement. The wages of
workers may be in dollars and the
consumption of meat in their families
may be in kilograms. The standard
deviation of wages in dollars cannot be
compared with the standard deviation of
amounts of meat in kilograms. Both the
standard deviations need to be converted
into coefficient of variation for
comparison. Suppose the value of CV for
wages is 10% and the value of CV for
kilograms of meat is25%. This means
that the wages of workers are consistent.