For example, suppose you are collecting data on the ages of people who attend a particular movie. You could decide to collect and report the exact age of everyone who attends. But this is likely to give you 60 or 70 different results, being every number from about 10 through 70 or 80. You may instead wish to collect data in groups, like “Under 20,” “20-29,” “30-39,” “40-49,” “50-59,” and “60 plus. ” This would be a more manageable set of six data groups. As another example, a doctor might collect body temperatures of patients on a given day. In this case, just collecting whole numbers, like 97, 98, 99, might not be precise enough. It might be necessary to report data in decimals in this case.
When you are sorting and rewriting your collection of data, be careful to include every point correctly. Count the data set to make sure you do not leave off any values.
x{\displaystyle x}. This column will be filled with each value that appears in your data set. Do not repeat items. For example, if the value 4 appears several times in the list, just put 4{\displaystyle 4} under the x{\displaystyle x} column once. n{\displaystyle n}, n(x){\displaystyle n(x)} or fr(x){\displaystyle fr(x)}. In statistics, the variable n{\displaystyle n} is conventionally used to represent the count of a particular value. You may also write n(x){\displaystyle n(x)}, which is read as “n of x,” and means the count of each x-value. A final alternative is fr(x){\displaystyle fr(x)}, which means the “frequency of x. ” In this column, you will put the number of times that the value appears. For example, if the number 4 appears three times, you will place a 3 next to the number 4. Relative Frequency or P(x){\displaystyle P(x)}. This final column is where you will record the relative frequency of each data item or grouping. The label P(x){\displaystyle P(x)}, which is read “P of x,” could mean the probability of x or the percentage of x. The calculation of relative frequency appears below. This column will be used after you complete that calculation for each value of x.
In the sample data set provided above, counting each item results in 16 total data points.
For example, in the data set provided above, consider the value 4{\displaystyle 4}. This value appears three times in the list.
Continuing with the example above, because the value 4{\displaystyle 4} appears three times, and the full set contains 16 items, you can determine that the relative frequency of the value 4{\displaystyle 4} is 3/16. This is equal to a decimal result of 0. 1875.
For example, using the data set above, the relative frequency table would appear as follows: x : n(x) : P(x) 1 : 3 : 0. 19 2 : 1 : 0. 06 3 : 2 : 0. 13 4 : 3 : 0. 19 5 : 4 : 0. 25 6 : 2 : 0. 13 7 : 1 : 0. 06 total : 16 : 1. 01
For example, the sample data set you have been working with includes all values from 1 to 7. But suppose that the number 3 never appeared. That could be important, and you would report the relative frequency of the value 3 as 0.
For example, the decimal result of 0. 13 is equal to 13%. The decimal result of 0. 06 is equal to 6%. (Don’t just skip over the 0. )
