Question

The table below shows 10 data values:

88

92

94

80

85

90

72

83

93

91



What is the five-number summary for these data?
Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94
Minimum = 80, Q1 = 85, median = 89, Q3 = 91, maximum = 93
Minimum = 80, Q1 = 83, median = 90, Q3 = 92, maximum = 93
Minimum = 72, Q1 = 85, median = 90, Q3 = 91, maximum = 94

Answer 1

The first step to do is to arrange the data set from least to greatest.

72 80 83 85 88 90 91 92 93 94

From the arrangement, we can see that the minimum is 72 and the maximum is 94. Next, the median is the middle number of the data. Since there are 10 data points, we take the average of the middle 2 numbers. The median is (88+90)/2 = 89.

When you talk about the quartiles, you draw divisions in your set. Q₁ is the middle data between the smallest and the median; Q₂ is the median; and Q₃ is the middle data between the largest and the median.


72 80 83 85 88 | 89 | 90 91 92 93 94

Q₁ is 83
Q₂ is 89
Q₃ is 92

Therefore, in summary, the answer is: Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94