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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.
You can use the definition of interquartile range and that of the range to compare both plots.
The statements that are true about given conditions are:
A: Ms. Dobson’s class has a smaller range of scores.
B: The district has a greater interquartile range.
C. Fifteen is an outlier for the district’s scores.
How does boxplot gives data?
The leftmost line tells the minimum value and rightmost line tells about the maximum value.
The box has 2 lines on either side telling position of first quartile(the left edge) and of third quartile(the right edge) and the middle line tells about the median of the data (it is second quartile)
What is interquartile range and range of data?
Range of a data plot = Maximum value of that data - minimum value of that data
Interquartile range of a data plot = Third Quartile - First Quartile
What is an outlier?
Outlier generally indicates those data points which are just too far from most of the data points. These points look like odd ones and lie outside.
We consider those data points outlier which are above third quartile + 1.5 times IQR or below first quartile - 1.5 times IQR
Using above definitions
For Ms Dobson's plot, we have:
Range = Max - Min = 95 - 40 = 55
IQR (Inter Quartile Range) = [tex]Q_3 - Q_1[/tex] = 80 - 70 = 10
Median = 75
For District wide plot, we have:
Range = Max - Min = 100 - 15 = 85
IQR = 75 - 55 = 20
Median = 65
Thus, we have:
A: Ms. Dobson’s class has a smaller range of scores. (55 < 85)
B: The district has a greater interquartile range. (10 < 20)
C. Fifteen is an outlier for the district’s scores.( 15 < 55 - 1.5 times 20= 25)
D is wrong since
[tex]55 - 1.5 \times 20 =25 < 100 < 75 + 1.5 \times 20 = 105[/tex]
25 < 100 < 105 (thus 100 is not below [tex]Q_1 - IQR[/tex] and not above [tex]Q_3 + IQR[/tex]
E is wrong since median of district plot is less than that of median of Ms Dobson's class plot (65 < 75) (we used median to represent the average score instead of mean since mean is not obtainable here and the best description we can use is median here).
Thus,
The statements that are true about given conditions are:
A: Ms. Dobson’s class has a smaller range of scores.
B: The district has a greater interquartile range.
C. Fifteen is an outlier for the district’s scores.
Learn more about box plot here:
https://brainly.com/question/1523909
