A professor grades a set of exams and then computes the quartiles: Q0 = 60. Q1 = 70. Q2 = 80 Q3 = 87. Q4 = 95

If the professor curves every grade up by 10 points, then how will Q2 be affected by the curve?

I. It will increase by 10 points
ii. It will be 10 points higher than the median for the noncurved data
III It will be halfway between Q1 and Q3 for the curved data

a. I only
b. II and III
c. I, II and III
d. I and II
e. I and III

Answer is c. I, II and II

Step-by-step explanation:

Solution:

Answer is c. I, II and II

It will be increase by 10 points and it will be 10 points higher than the median for the noncurved data. and it will be halfway between Q1 and Q3 for the curved data.

Median for noncurved data = Q2 = 80

Median for curved data = 90

It will increase by 10 points = 90  

It will be 10 points higher than the noncurved data = 90-80 = 10 points

if the set contains 20 values then, noncurved data will be:

60 _ _ _ _ 70 _ _ _ _ 80 _ _ _ _ 87 _ _ _ _ 95

Curved data will be: (all grades increased by 10 points)

70 _ _ _ _ 80 _ _ _ _ 90 _ _ _ _ 97 _ _ _ _ 105

Here, we can see median = Q2 = 90, exactly, halfway between Q1 =80 and Q3 = 97

Hence, C is the right answer