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230 Part IV: Quality AssuranceContinuedb. Having completed the frequency distribution table, we are ready to construct thehistograms. To construct the frequency histogram we first mark the classes on the x-axisand the frequencies on the y-axis. Remember that when we mark the classes on thex-axis we must make sure there is no gap between the classes. Then on each classmarked on the x-axis, place a rectangle so that the height of each rectangle is proportionalto the frequency of the corresponding class. The frequency histogram for thedata with a frequency distribution as given in Table 18.9 is shown in Figure 18.15.To construct the relative frequency histogram, just change the scale on the y-axisin Figure 18.15 so that instead of plotting the frequencies, we can plot relative frequencies.The resulting graph shown in Figure 18.16 is the relative frequency histogram forthe data with the relative frequency distribution given in Table 18.9.10Frequency5030 54 78 102 126 150 174 198DataPart IV.A.4Figure 18.15Frequency histogram for survival time of parts under extreme operatingconditions.10/50Relative frequency5/500.030 54 78 102 126 150 174 198DataFigure 18.16Relative frequency histogram for survival time of parts under extremeoperating conditions.
Chapter 18: A. Basic Statistics and Applications 23110Frequency5030 54 78 102 126 150 174 198DataFigure 18.17 Frequency polygon for the data in Example 18.23.10/50Relative frequency5/50030 54 78 102 126 150 174 198DataFigure 18.18 Relative frequency polygon for the data in Example 18.23.Part IV.A.4polygon and the relative frequency polygon for the data in Example 18.23 areshown in Figure 18.17 and Figure 18.18 respectively.Sometimes a data set consists of a very large number of observations, whichresults in having a large number of classes of very small widths. In such casesfrequency polygons or relative frequency polygons become very smooth curves.For example, Figure 18.19 shows one such smooth curve.Such curves are usually called frequency distribution curves, which representthe probability distributions of continuous random variables. Thus, histogramseventually become the basis of probability distributions.The shape of the frequency distribution curve depends on the shape of its correspondinghistogram that, in turn, depends on the given set of data. The shape ofa frequency distribution curve, in fact, can be of any type, but in general, there arethree types of frequency distribution curves as shown in Figure 18.20.
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230 Part IV: Quality Assurance
Continued
b. Having completed the frequency distribution table, we are ready to construct the
histograms. To construct the frequency histogram we first mark the classes on the x-axis
and the frequencies on the y-axis. Remember that when we mark the classes on the
x-axis we must make sure there is no gap between the classes. Then on each class
marked on the x-axis, place a rectangle so that the height of each rectangle is proportional
to the frequency of the corresponding class. The frequency histogram for the
data with a frequency distribution as given in Table 18.9 is shown in Figure 18.15.
To construct the relative frequency histogram, just change the scale on the y-axis
in Figure 18.15 so that instead of plotting the frequencies, we can plot relative frequencies.
The resulting graph shown in Figure 18.16 is the relative frequency histogram for
the data with the relative frequency distribution given in Table 18.9.
10
Frequency
5
0
30 54 78 102 126 150 174 198
Data
Part IV.A.4
Figure 18.15
Frequency histogram for survival time of parts under extreme operating
conditions.
10/50
Relative frequency
5/50
0.0
30 54 78 102 126 150 174 198
Data
Figure 18.16
Relative frequency histogram for survival time of parts under extreme
operating conditions.