EXAMPLE 13 Finding the ranks of combined data and summing the ranks for each sample

The following table shows the pulse rates in beats per minute for a random sample of five women and a random sample of four men.

  1. Combine the data sets and find the ranks.
  2. Find the sum of the ranks for the women and the sum of the ranks for the men.
    Women 66 77 57 62 68
    Men 79 71 68 71

Solution

  1. We temporarily combine the two samples and arrange the values in increasing order. We then rank the data values from smallest to largest, as shown in the following table. Note that we have two pulse rates of 68 beats per minute. Had these not been tied, they would have had ranks 4 and 5. We therefore assign to each the mean rank . Similarly, the two pulse rates of 71 beats per minute are assigned the mean rank .

    14-30

    Combined data 57 62 66 68 68 71 71 77 79
    Rank 1 2 3 4.5 4.5 6.5 6.5 8 9

  2. The sum of the ranks for the women is

    The sum of the ranks for the men is

NOW YOU CAN DO

Exercises 7–10.