Raw Frequency Tables

Raw Frequency Tables

Twenty students were asked how many hours they worked per day. Their responses, in hours, are as follows: 5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6, 5, 4, 4, 3, 5, 2, 5, 3.

The following table lists the different data values in ascending order and their frequencies.

A frequency is the number of times a value of the data occurs. According to the table, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample.

A relative frequency is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample–in this case, 20. Relative frequencies can be written as fractions, percents, or decimals.

Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in the table below.

The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.

When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these.

Some people add a cumulative frequency and a percentage column to their frequency tables. This is not so hard to do!

Calculating cumulative frequency is very similar to calculating cumulative relative frequency. Instead of adding all the previous relative frequencies to the relative frequency for the current row, you add all of the previous frequencies to the frequency for the current row. The cumulative frequency tells you how many people score at or below a given value.

Finally, adding a percentage column can be done by just multiplying the cumulative relative frequency by 100. Note that the final number in the cumulative relative frequency column is always 1. When we are talking about percentages that number is always 100 (1x100 =100). This makes sense because by the time we reach the final row in our table, we should have accounted for 100% of our data.

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