Page 163 - DMGT501_OPERATIONS_MANAGEMENT

Unit 6: Quality Assurance and Control

been met, then the life span of the third part to fail can sometimes be used to predict the average Notes
of all five, and thereby the result of the test becomes much sooner.

Dispersion

The extent to which the data are scattered about the zone of central tendency is known as the
dispersion. Measure of dispersion is the second of the two most fundamental measures in
statistical analysis.
Followings are the measures of dispersion, Range, Variance and Standard Deviation, Mean
Deviation, Coefficient of Variation.
1. Range: The simplest measure of dispersion in a sample is the range which is defined as the
difference between the largest and the smallest values included in the distribution.
Range = largest value minus smallest value = R. The advantage of the range as a measure
of dispersion is its utmost simplicity. However, the range can sometimes be misleading
because of the effect of just one extreme value.
The range is the most commonly used measure of dispersion in every day life. Examples
are:
(a) In weather forecast min. and max. temp. in a day.
(b) In SPC (Statistical Process Control) mean and range charts.
(c) Used in studying variation in money rates, share prices.

2. Variance and Standard Deviation: A second measure of dispersion is the variance.
This is defined as the measure of dispersion about the mean and is determined by squaring
each deviation, adding these squares (all of which necessarily have plus signs) and dividing
by the number of them.
d 2
Expressed as a formula: i
n
where d = (x – x) is the deviation from the mean.
i i
While the variance is of fundamental importance in statistical analysis, the most useful
measure of dispersion is the square root of the variance, known as the “standard deviation”.
It is easily seen that when the data is in the form of a frequency distribution:
Std. Deviation = = sq. of Variance

d 2
= sq. of i
n
When the frequency of the variable is given (f)
Std. Deviation = r = sq. root of Variance

fd 2
= sq. root of i i
n
3. Mean Deviation: Mean Deviation in a set of observations is the arithmetic average of the
deviations of each individual observation from a measure of the central tendency (mean,
mode, median).

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