Question

The table shows the hourly cookie sales by students in grades 7 and 8 at the school's annual bake sale. Grade 7 Grade 8 20 21 15 29 30 14 24 19 18 24 21 25 The interquartile range for the grade 7 data is The interquartile range for the grade 8 data is The difference of the medians of the two data sets is The difference is about times the interquartile range of either data set.

Answer 1

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)

$Q_1=18, Median=\frac{20+21}{2}=20.5, Q_3=24$

The interquartile range for the grade 7 data is

$IQR=Q_3-Q_1=24-18=6$

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)

$Q_1=19, Median=\frac{21+24}{2}=22.5, Q_3=25$

The interquartile range for the grade 8 data is

$IQR=Q_3-Q_1=25-19=6$

Therefore the interquartile range for the grade 8 data is 6.

The difference of the medians of the two data sets is

$D=22.5-20.5=2$

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.

$D=x(IQR)$

$2=x(6)$

$\frac{2}{6}=x$

$\frac{1}{3}=x$

Therefore the difference is about 1/3 times the interquartile range of either data set.