The line graph shows the daily wages of employees at a company. Using the graph, complete the frequency table.
Looking at the table, we can see that the wages have been grouped into categories. The first group includes every employee whose wage is from 20 Egyptian pounds up to but not including 30 Egyptian pounds. The second group is for those employees whose wage is 30 Egyptian pounds up to but not including 40 Egyptian pounds, and so it continues for the rest of the groups.
The points in the line graph have been plotted at the midpoint of each group. As in a frequency polygon, we plot the midpoint against the frequency. The midpoint for the first group is 25. In order to determine the frequency for this group, we need to read the value on the vertical axis. The frequency for this group is four.
The midpoint for the next group, which is from 30 up to not including 40 Egyptian pounds, is 35. Reading horizontally across to the frequency axis from this point, we see that the frequency in the 30-to-40 group is five. The midpoint for the next group is 45.
Again reading vertically up to the line graph from this point and then across to the frequency axis, we see that the frequency for the 40-to-50 group is 14. The midpoints for the next group, which is 50 up to but not including 60, is 55. Reading up from this value to the graph and then across to the frequency axis, we see that the frequency is 12.
For the final group, which is 60 up to but not including 70, the midpoint is 65. Reading from the graph at this point, we see that the frequency for this group is five. So we’ve now filled in the five frequencies for the five groups.
Remember we’re told that the total is 40. So a sensible check at this stage would be to add together our frequencies and check that they do indeed sum to 40.
The sum of our five frequencies, four plus five plus 14 plus 12 plus five, is indeed equal to 40. The values in the completed frequency table are four, five, 14, 12, and five.