a. A cumulative diagram to show this information is shown in the image attached below.
b. The median delivery distance is equal to 11 km. The interquartile range of the delivery distance is 6 km.
In Mathematics and Statistics, the cumulative frequency of a data set can be calculated by adding each frequency from a frequency distribution table to the sum of the preceding frequency.
Based on the frequency distribution table, we have the following cumulative frequency table:
Distance (km) Cumulative frequency
5 8
10 30
15 70
20 80
Part b.
The second quartile is sometimes referred to as the median, or 50th percentile (50%). This ultimately implies that, the median number is the middle of any data set;
Median delivery distance ≈ 11 km
Interquartile range (IQR) of data set = third quartile - first quartile
Interquartile range (IQR) of data set = 13 - 7
Interquartile range (IQR) of data set = 6 km.