3. 3
Measure of variability (dispersion):-
• Measures of variability describe how spread out the values are in a
distribution of values.
• When describing a variable, it is important to describe both its measure
of central tendency and its measure of dispersion.
• The five most commonly used measures of dispersion are the range,
interquartile range, variance, standard deviation, and coefficient
of variation.
• Measure of dispersion depends on the measurement scale of the
variable.
4. 4
Range:
• The range is the difference between the maximum value and
minimum value of a variable.
• The range is used when you have ordinal data or you are
presenting your results to people with little or no knowledge of
statistics.
• The range is rarely used in scientific work as it is fairly
insensitive.
• For example, in a sample there might be five subjects ages:
10, 14, 20, 55, and 95.
The age range of the sample = 95 - 10 = 85 years
5. 5
Standard deviation:
• The standard deviation is a measure that indicates the average
deviation or variability of all the values from the mean of a set of
values.
• The standard deviation is the most widely used measure of
variability when interval or ratio data are described.
• When the standard deviation is large, the spread among the
values in the data set is large, indicating a heterogeneous
sample.
• When the deviation is small, most of the scores are very close
to the average score, indicating a more homogeneous
sample.
9. 9
Computing the variance and standard deviation
Step 1: Compute the sum of the squared deviations about
the mean = 10543.6
Step 2: Divide by the sample size n - 1.
10543.6 / (10-1) = 10543.6 /9 = 1171.511
Since:
