Question

Jessie received the following scores on her math tests this year. (45, 65, 70, 80, 85, 100) Suppose the teacher removes the lowest and highest scores. (65, 70, 80, 85) What are the interquartile ranges of Jessie’s original scores and her new scores?

Answer 1

Original scores :
45,65,70,80,85,100
IQR = 85 - 65 = 20

new scores :
65,70,80,85
IQR = (80 + 85)/2 - (65 + 70)/2 = 82.5 - 67.5 = 15

Answer 2

Answer:

Interquartile ranges of Jessie’s original scores = 20

Interquartile ranges of Jessie’s new scores = 15

Step-by-step explanation:

Interquartile range IQR = Higher quartile (Q3) - lower quartile (Q1)

Where Q3 is the mid-value of the second half of a dataset and

Q1 is the mid-value of the first half of a dataset.

Original score = 45, 65, 70, 80, 85, 100

Q1 of original score:

First half of original score = 45, 65, 70

Therefore Q1 = 65

Q3 of original score:

Second half of original score = 80, 85, 100

Therefore Q3 = 85

:. Interquartile range IQR of original score = Q3 of original score - Q1 of original score

:. IQR = 85 - 65 = 20

New score = 65, 70, 80, 85

Q1 of new score:

First half of new score = 65, 70

Therefore Q1 = (65+70)/2 = 67.5

Q3 of new score:

Second half of new score = 80, 85

Therefore Q3 = (80 + 85)/2 = 82.5

:. Interquartile range IQR of new score = Q3 of new score - Q1 of new score

:. IQR = 82.5 - 67.5 = 15

Therefore:

Interquartile ranges of Jessie’s original scores = 20

Interquartile ranges of Jessie’s new scores = 15