We need to give the five-number summary and the interquartile range. To do this, we'll make sure that the data values are ordered from least to greatest.
54
56
58
59
62
62
64
70
76
76
80
81
We'll start with the minimum and maximum. The minimum is 53. The maximum is 81.
Next, we'll find the median. Since there are 13 data values, the median will be the 7th value. In this case, the median is 62.
To find the lower quartile, we'll take the median of the lower half of the data set. Since there are 6 data values in the lower half, the lower quartile will be the 3rd value. In this case, the lower quartile is 56.
To find the upper quartile, we'll take the median of the upper half of the data set. Since there are 6 data values in the upper half, the upper quartile will be the 3rd value. In this case, the upper quartile is 76.
Finally, we can find the interquartile range by subtracting the lower quartile from the upper quartile. In this case, the interquartile range is 76 - 56 = 20.