Q:

Why are unequal class intervals sometimes used in a frequency distribution?

A:

Unequal class intervals can be used in frequency distribution if the rate of occurrence is very unevenly distributed, with certain classes showing far lower or far greater frequencies than those on either side. In many data tables and histograms, consistent intervals are used, but they cannot always account for irregularities and outliers like those that strategically use unequal intervals.

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Wikipedia explains that frequency distribution is a representation of data in a grouped fashion that illustrates how often a particular interval is represented within a corresponding string of ungrouped data.

For example, the frequency distribution of times to finish a race might show the following:

40-50 seconds: 4 runners

50-60 seconds: 9 runners

60-70 seconds: 2 runners

Equal intervals work very well for tables that do not represent a large range or great amount of values. Math Is Fun shows that they can be easily converted into a histogram, which is like a bar graph but has connected bars that mark intervals instead of individual values.

However, with some larger sets of data, even intervals do not accurately reflect the findings in the experiment. For example, if all the students in a high school had their race times recorded, the distribution is extremely different. Clusters of students can form around the 1- and 2-minute marks, but there could be extreme outliers, such as those who decided to walk instead of run.

The data table can show the following:

0-60 seconds: 58

60-120 seconds: 462

120-180 seconds: 321

180-240 seconds: 72

240-300 seconds: 26

300-360 seconds: 61

However, because no one ran it in under 40 seconds and because there were no values represented between 3.5 and 4.5 minutes, the above frequency distribution is not very representative.

The following distribution in 20-second intervals presents a more accurate picture:

40-60 seconds: 58

60-80 seconds: 201

80-100 seconds: 179

100-120 seconds: 82

120-140 seconds: 185

140-160 seconds: 76

160-180 seconds: 60

180-200 seconds: 72

*200-280 seconds: 0

280-300 seconds: 26

300-320 seconds: 43

320-340 seconds: 18

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In math, the frequency is the number of times a specific value appears in a data set or list. To find the frequency of these values, one constructs a frequency table and inputs all the different values from the set.