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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)
[tex]Q_1=18, Median=\frac{20+21}{2}=20.5, Q_3=24[/tex]
The interquartile range for the grade 7 data is
[tex]IQR=Q_3-Q_1=24-18=6[/tex]
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)
[tex]Q_1=19, Median=\frac{21+24}{2}=22.5, Q_3=25[/tex]
The interquartile range for the grade 8 data is
[tex]IQR=Q_3-Q_1=25-19=6[/tex]
Therefore the interquartile range for the grade 8 data is 6.
The difference of the medians of the two data sets is
[tex]D=22.5-20.5=2[/tex]
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.
[tex]D=x(IQR)[/tex]
[tex]2=x(6)[/tex]
[tex]\frac{2}{6}=x[/tex]
[tex]\frac{1}{3}=x[/tex]
Therefore the difference is about 1/3 times the interquartile range of either data set.
The interquartile range for grade 7 is 6.
The interquartile range for grade 8 is 6
The difference between the medians of the two data sets is 2.
The difference is about 1/3 times the interquartile range of either data set.
Given that
The table shows the hourly cookie sales by students in grades 7 and 8 at the school's annual bake sale.
Grade 7 20 15 30 24 18 21
Grade 8 21 29 14 19 24 25
We have to determine
The interquartile range for the grade 7 data is.
The interquartile range for the grade 8 data is.
The difference between the medians of the two data sets is.
The difference is about times the interquartile range of either data set.
According to the question
1. The interquartile range for the grade 7 data is given by,
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 into four equal parts.
(15), 18, (20), (21), 24,( 30)
Then
The interquartile range for grade 7 is,
= 24 -18 = 6
The interquartile range for grade 7 is 6.
2. 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 into four equal parts.
(14), 19, (21), (24), 25, (29)
Then
The interquartile range for grade 8 is,
= 25- 19 = 6
The interquartile range for grade 8 is 6.
3. The difference between the medians of the two data sets is,
[tex]\rm Median = \dfrac{Grade \ 8- Grade \ 7}{2}\\ \\ Median = \dfrac{(24+21) - (21+20)}{2}\\ \\ Median = \dfrac{24+21-21-20}{2}\\ \\ Median = \dfarc{24-20}{2}\\ \\ Median = \dfrac{4}{2}\\ \\ Median = 2[/tex]
The difference between the medians of the two data sets is 2.
4. The difference is about times the interquartile range of either data set.
The IQR of each data is 6.
[tex]\rm Difference = x \times Interquartile range\\\\2 = x \times 6\\\\x = \dfarc{2}{6}\\\\x = \dfrac{1}{3}[/tex]
The difference is about 1/3 times the interquartile range of either data set.
To know more about the Interquartile range click the link given below.
https://brainly.com/question/4330753
