Answer:
1. The interquartile range for the grade 7 data is 6.
2. The interquartile range for the grade 8 data is 6.
3. The difference of the medians of the two data sets is 2.
4. The difference is about 1/3 times the interquartile range of either data set.
Step-by-step explanation:
The hourly cookie sales by students in grades 7 and 8 at the school's annual bake sale is given by the following table.
Grade 7 Grade 8
20 21
15 29
30 14
24 19
18 24
21 25
The data set for grade 7 is
20, 15, 30, 24, 18, 21
Arrange the data in ascending order.
15, 18, 20, 21, 24, 30
Divide the data in four equal parts.
(15), 18, (20), (21), 24,( 30)
The interquartile range for the grade 7 data is
Therefore the interquartile range for the grade 7 data is 6.
The data set for grade 8 is
21, 29, 14, 19, 24, 25
Arrange the data in ascending order.
14, 19, 21, 24, 25, 29
Divide the data in four equal parts.
(14), 19, (21), (24), 25, (29)
The interquartile range for the grade 8 data is
Therefore the interquartile range for the grade 8 data is 6.
The difference of the medians of the two data sets is
Therefore the difference of the medians of the two data sets is 2.
Let the difference is about x times the interquartile range of either data set.
The IQR of each data is 6.
Therefore the difference is about 1/3 times the interquartile range of either data set.