Answers:
A. Ms. Dobson’s class has a smaller range of scores;
B. The district has a greater interquartile range; and
C. Fifteen is an outlier for the district’s scores.
Explanation:
The scores for Ms. Dobson's class go from the lowest of 40 to the highest of 95; this is a range of 95-40 = 55. The scores for the district go from the lowest of 15 to the highest of 100; this is a range of 100-15 = 85. Ms. Dobson's class has a smaller range of scores.
The interquartile range (IQR) is found by subtracting Q3, the third quartile, and Q1, the first quartile.
For Ms. Dobson's class, Q1 is 70 and Q3 is 80; this makes the IQR 80-70 = 10. For the district, Q1 is 55 and Q3 is 75; this makes the IQR 75-55 = 20. The district has a greater interquartile range.
An outlier is any value that is less than 1.5 times the interquartile range below Q1 or greater than 1.5 times the interquartile range above Q3.
For the district, Q1 is 55 and the IQR is 20; any outlier would be less than
55-1.5(20) = 55-30 = 25. 15 is less than 25, so it would be an outlier.
For the district, Q3 is 75 and the IQR is 20; any outlier would be greater than 75+1.5(20) = 75+30 = 105; there are no values in the district's scores this high or more; 100 is not an outlier for this set.
Ms. Dobson's class had scores that were overall higher than the district. While the district had a few that were higher, the scores for Ms. Dobson's class were clustered higher than those of the district.
