Doctor 2

A doctor noted the Diastolic Blood Pressure (DBP) of a large number of patients. Later, he scrambled the data to keep the privacy of his patients. Based on the scrambled dataset, he finds that the lower inner fence is equal to 50 and the upper inner fence is equal to 100. Find the IQR value, which is the difference between the third and the first quartile.

Correct answer:

i =  12.5

Step-by-step explanation:

a - 1.5·i = 50
b + 1.5·i = 100
i = b-a

a-1.5i = 50
b+1.5i = 100
a-b+i = 0

Row 3 - Row 1 → Row 3
a-1.5i = 50
b+1.5i = 100
-b+2.5i = -50

Row 3 + Row 2 → Row 3
a-1.5i = 50
b+1.5i = 100
4i = 50


i = 50/4 = 12.5
b = 100-1.5i = 100-1.5 · 12.5 = 81.25
a = 50+1.5i = 50+1.5 · 12.5 = 68.75

a = 275/4 = 68.75
b = 325/4 = 81.25
i = 25/2 = 12.5

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