The number of calls from motorists per day for roadside service was recorded for the month of December 2003.  The result

Solution

To construct a frequency table, we proceed as follows:

Small data value = 28

Highest data value = 217

Difference = Highest value – Smallest value

= 217 – 28

= 189

Let the width of the class interval be 40.

∴ Number of class intervals = (Round up to the next integer)

There are at least 5 class intervals. This is reasonable for the given data.

Step 1:  Construct a table with three columns, and then write the data groups or class intervals in the first column.  The size of each group is 40.  So, the groups will start at 0, 40, 80, 120, 160 and 200 to include all of the data.  Note that in fact we need 6 groups (1 more than we first thought).

Step 2:  Go through the list of data values.  For the first data value in the list, 28, place a tally mark against the group 0-39 in the second column.  For the second data value in the list, 122, place a tally mark against the group 120-159 in the second column.  For the third data value in the list, 217, place a tally mark against the group 200-239 in the second column.

We continue this process until all of the data values in the set are tallied.

Step 3:  Count the number of tally marks for each group and write it in the third column.  The finished frequency table is as follows:

To find the mean of a large set of data values, we can use a frequency table.  Add an extra column to the frequency table and label it Frequency × Data Value.  Then calculate the sum of the values in this fourth column and use it to find the mean.