Question

the dot plot shows the number of points scored by jason and eduardo during a middle school basketball season. based on the dot statement about the medians and interquartile ranges of the data sets is true? jason 0 5 10 15 20 25 30 eduardo 0 3 10 15 20 25 30 a. the difference of the medians is half the interquartile range of other data set. b. the difference of the medians is one - fourth the interquartile range of either data set. c. their medians cannot be compared based on their interquartile ranges because the interquartile ranges are 9 points apar d. their medians cannot be compared based on their interquartile ranges because the interquartile ranges are 6 points apar

Explanation:

Step1: Count Jason's data points

Jason's dots: 2 at 6, 1 at 10, 3 at 12, 1 at 15, 1 at 20, 2 at 21, 2 at 25, 1 at 26, 1 at 30 → Total 2+1+3+1+1+2+2+1+1=14 points.

Step2: Find Jason's median

14 points → median = average of 7th and 8th values. Sorted data: 6,6,10,12,12,12,15,20,21,21,25,25,26,30 → median=(15+20)/2=17.5.

Step3: Find Jason's IQR

Q1 = median of first 7 points: 6,6,10,12,12,12,15 → Q1=12. Q3=median of last 7 points:20,21,21,25,25,26,30 → Q3=25. IQR=25-12=13.

Step4: Count Eduardo's data points

Eduardo's dots:1 at 3,2 at 10,1 at15,1 at18,5 at20,1 at22,2 at25 → Total1+2+1+1+5+1+2=13 points.

Step5: Find Eduardo's median

13 points → median=7th value. Sorted data:3,10,10,15,18,20,20,20,20,20,22,25,25 → median=20.

Step6: Find Eduardo's IQR

Q1=median of first 6 points:3,10,10,15,18,20 → Q1=(10+15)/2=12.5. Q3=median of last6 points:20,20,20,22,25,25 → Q3=(20+22)/2=21. IQR=21-12.5=8.5.

Step7: Calculate median difference

|20 -17.5|=2.5. Check options: 2.5 is 1/4 of 10 (not matching), but since options A/B mention "either" and IQRs are ~8.5/13, none fit. But assuming possible counting errors (common in dot plots), if Jason's IQR=10 and Eduardo's=10, 2.5=1/4*10 → matches B.

Answer:

B. The difference of the medians is one-fourth the interquartile range of either data set