Question

2 the stem and leaf plots below show the grades for an exam in two different math classes taught by the same professor at different times of day
(a) find the 5 - number summary of each of the classes. 1st class: __________ 2nd class: __________
(b) find the interquartile range for each of the classes. 1st class iqr = __________ 2nd class iqr = __________
(c) find any potential outlier(s). 1st class outlier(s) (if any) = __________ 2nd class outlier(s) (if any) = __________

Explanation:

Step1: List 1st class data

25,35,35,36,38,38,42,44,45,45,47,53,58,59,62,70,71,83,84,87,94,95,95,96,96,97,97,100,100,100,100,100 (n=32)

Step2: 1st class 5-number summary

min=25; Q1=(44+45)/2=44.5; median=(70+71)/2=70.5; Q3=(96+96)/2=96; max=100

Step3: List 2nd class data

21,33,37,42,44,53,53,56,57,60,61,61,65,65,65,67,68,68,69,74,76,76,77,78,78,84,87,93,100 (n=29)

Step4: 2nd class 5-number summary

min=21; Q1=(53+56)/2=54.5; median=65; Q3=76; max=100

Step5: Calculate 1st class IQR

IQR=Q3-Q1=96-44.5=51.5

Step6: Calculate 2nd class IQR

IQR=76-54.5=21.5

Step7: Check 1st class outliers

Bounds: 44.5-1.5×51.5=-32.75, 96+1.5×51.5=173.25; no outliers

Step8: Check 2nd class outliers

Bounds: 54.5-1.5×21.5=22.25, 76+1.5×21.5=108.25; 21 < 22.25 (outlier)

Answer:

(a) 1st class: 25, 44.5, 70.5, 96, 100; 2nd class: 21, 54.5, 65, 76, 100
(b) 1st class IQR = 51.5; 2nd class IQR = 21.5
(c) 1st class outlier(s) (if any) = None; 2nd class outlier(s) (if any) = 21