Additional Statistical Terminology
Here are some more definitions you should learn in order to get comfortable reading or talking about statistics.
Cumulative Absolute Frequency
When data are tabulated, the absolute frequencies are often shown in one or more columns. Look at Table 7-5, for example. This shows the results of the tosses of the blue die in the experiment we looked at a while ago. The first column shows the number on the die face. The second column shows the absolute frequency for each face, or the number of times each face turned up during the experiment. The third column shows the cumulative absolute frequency , which is the sum of all the absolute frequency values in table cells at or above the given position.
Table 7-5 Results of an experiment in which a “weighted” die is tossed 6000 times, showing absolute frequencies and cumulative absolute frequencies.
Face of die |
Absolute frequency |
Cumulative absolute frequency |
1 |
380 |
380 |
2 |
268 |
648 |
3 |
408 |
1056 |
4 |
1287 |
2343 |
5 |
1599 |
3942 |
6 |
2058 |
6000 |
The cumulative absolute frequency numbers in a table always ascend (increase) as you go down the column. The highest cumulative absolute frequency value should be equal to the sum of all the individual absolute frequency numbers. In this instance, it is 6000, the number of times the blue die was tossed.
Find practice problems and solutions at Mean, Median, Mode and Cumulative Frequency: Practice Problems - Set 1.
Cumulative Relative Frequency
Relative frequency values can be added up down the columns of a table, in exactly the same way as the absolute frequency values are added up. When this is done, the resulting values, usually expressed as percentages, show the cumulative relative frequency .
Examine Table 7-6. This is a more detailed analysis of what happened with the blue die in the above-mentioned experiment. The first, second, and fourth columns in Table 7-6 are identical with the first, second, and third columns in Table 7-5. The third column in Table 7-6 shows the percentage represented by each absolute frequency number. These percentages are obtained by dividing the number in the second column by 6000, the total number of tosses. The fifth column shows the cumulative relative frequency, which is the sum of all the relative frequency values in table cells at or above the given position.
The cumulative relative frequency percentages in a table, like the cumulative absolute frequency numbers, always ascend as you go down the column. The total cumulative relative frequency should be equal to 100%. In this sense, the cumulative relative frequency column in a table can serve as a checksum , helping to ensure that the entries have been tabulated correctly.
Table 7-6 Results of an experiment in which a “weighted” die is tossed 6000 times, showing absolute frequencies, relative frequencies, cumulative absolute frequencies, and cumulative relative frequencies.
Face of die |
Absolute frequency |
Relative frequency |
Cumulative absolute frequency |
Cumulative relative frequency |
1 |
380 |
6.33% |
380 |
6.33% |
2 |
268 |
4.47% |
648 |
10.80% |
3 |
408 |
6.80% |
1056 |
17.60% |
4 |
1287 |
21.45% |
2343 |
39.05% |
5 |
1599 |
26.65% |
3942 |
65.70% |
6 |
2058 |
34.30% |
6000 |
100.00% |
Find practice problems and solutions at Mean, Median, Mode and Cumulative Frequency: Practice Problems - Set 2.
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