Reference
Work sampling
“Work sampling” is a means of analyzing equipment, working hours, and other details. After an observation frequency is chosen, the working status of particular employees is monitored at random intervals.
(2)Data dispersion
“Data dispersion” numerically represents the extent of spread in individual sets of data around a particular mean.
Even in cases where collections of data bear the same mean, their properties may differ as shown below.
Data
Mean
Group A
20, 21, 22, 19, 18
20+21+22+19+18
=20
5
Group B
10, 30, 5, 25, 30
10+30+5+25+30
=20
5
Values that express these differences include “variance,” “standard deviation,” and “range,” each of which serves as a dispersion index.
Value
Explanation
Variance
The value calculated by subtracting the mean from the value of each
data set, squaring that result, adding each of those figures together,
and dividing the total sum by the number of data sets.
Standard
deviation
The value derived from the square root of the variance.
Range
The difference between the highest and lowest numbers contained in
the data.
Although Group A and Group B have the same mean, data dispersion is
calculated as follows.
Group A
Group B
Mean
20
20
Variance
{(20−20)2+(21−20)2+(22−20)2
2
2
+(19−20) +(18−20) }÷5
=(0+1+4+1+4)÷5
=10÷5
=2
{(10−20)2+(30−20)2+(5−20)2+
(25−20)2+(30−20)2}÷5
=(100+100+225+25+100)÷5
=550÷5
=110
Standard
deviation
Range
2≒1.414
22−18=4
110≒10.48
30−5=25
With the mean alone, it is not possible to accurately analyze how data is
structured. Through dispersion, a strong understanding of the data’s overall
distribution can be gained.
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