The data for each grade have the same interquartile range (IQR). Which of the following best compares the two best score distributions? With reference

fortdefruitI 2021-02-13 Answered
The data for each grade have the same interquartile range (IQR). Which of the following best compares the two best score distributions?
With reference to line plots the data for Sixth grade geography test score is
7 8 8 9 9 9 9 9 10 10 10 11 11 11 12 12 12 14 14 15
The data of seventh grade geography test score is
7 10 10 11 11 11 11 12 12 13 13 13 13 13 14 14 14 15 16 17
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Expert Answer

faldduE
Answered 2021-02-14 Author has 109 answers

The median is the middle value of the data distribution. Here there are 20 data points for sixth and seventh grade test scores each. So the median will be the average of 10th and 11th data point when arranged in ascending order.
The median of sixth grade geography test score is calculated as shown below
10th data point =10
11th data point =10
Median = 10+102=10
The median of seventh grade geography test score is calculated as shown below
10th data point =13
11th data point =13
Median =13+132=13
The IQR is difference between Quartile 3 and Quartile 1.
For sixth grade geography test scores
7 8 8 9 9 9 9 9 10 10 10 11 11 11 12 12 12 14 14 15
The Quartile 1 divide the data distribution in such way that 25% of data lie less than it and 75% lie more than it. In a way we can say it is median of first half of data distribution.
Quartile 1 is average of 5th and 6th data points when arranged in ascending order
Q1=9+92=9
The Quartile 3 divide the data distribution in such way that 75% of data lie less than it and 25% lie more than it. In a way we can say it is median of second half of data distribution.
Quartile 3 is average of 15th and 16th data points when arranged in ascending order
Q1=12+122=12
Inter Quartile Range =Q3Q1=129=3
For seventh grade geography test scores
7 10 10 11 11 11 11 12 12 13 13 13 13 13 14 14 14 15 16 17
The Quartile 1 divide the data distribution in such way that 25% of data lie less than it and 75% lie more than it. In a way we can say it is median of first half of data distribution.
Quartile 1 is average of 5th and 6th data points when arranged in ascending order
Q1=11+112=11
The Quartile 3 divide the data distribution in such way that 75% of data lie less than it and 25% lie more than it. In a way we can say it is median of second half of data distribution.
Quartile 3 is average of 15th and 16th data points when arranged in ascending order
Q1=14+142=14
Inter Quartile Range =Q3Q1=1411=3
Thus the median of Seventh grade is 13 and median of sixth grade is 10, while the Inter quartile range for both of them is 3. So option 3 is correct.
The median score of the seventh grade class is 3 points greater than the median score of the sixth grade class. The difference is the same as the IQR.

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