Question

The table shows data for a class's mid-term and final exams Which data set has the largest IQR?

Mid-Term Final
100 98
100 95
100 93
95 91
95 88
92 82
92 78
88 78
85 65
75 60

Answer 1

Putting the numbers in order;

Mid-term numbers: 100 100 100 95 95 92 92 88 85 75

Median = (95 + 92) / 2 = 93.5

First quarter = Q1 = 100 100 100 95

Median of first quarter = (100 + 100) / 2 = 100

Third quarter = Q3 = 92 88 85 75

Median of third quarter = (88 + 85) / 2 = 86.5

Interquartile range (IQR) can be calculated by subtracting Q3 from Q1;

IQR of mid-term = 86.5 – 100 = -13.5

Now putting the final term numbers in order;

Final-term numbers: 98 95 93 91 88 82 78 78 65 60

Median = (88 + 82) / 2 = 85

First quarter = Q1 = 98 95 91 88

Median of first quarter = (95 + 91) / 2 = 93

Third quarter = Q3 = 78 78 65 60

Median of third quarter = (78 + 65) / 2 = 71.5

Interquartile range (IQR) can be calculated by subtracting Q3 from Q1;

IQR of final-term = 71.5 – 93 = -21.5

Thus the IQR of mid-term is the largest.