4 measures of variability

Biostatistics

1. MEASURES OF VARIABILITY
(DISPERSION)
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College of Nursing
3
rd
stage
Biostatistics
Dr. Nazar A. Mahmood

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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.

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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

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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.

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Standard deviation formula

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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:

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