Ten students achieve the following test scores on an exam: 78, 69, 45, 89, 74, 37, 99, 77, 100, 82. What is the interquartile range of these scores?
Arrange the scores in numerical order. The middle scores form the interquartile range.
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Ten students achieve the following test scores on an exam: 78, 69, 45, 89, 74, 37, 99, 77, 100, 82. What is the interquartile range of these scores?
To find the interquartile range (IQR), we first need to determine the lower quartile (Q1) and the upper quartile (Q3).
Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half.
Step 1: Arrange the data in ascending order:
37, 45, 69, 74, 77, 78, 82, 89, 99, 100
Step 2: Find the median (Q2):
Since there are 10 data points, the median is the average of the 5th and 6th values.
Median = (77 + 78) / 2 = 77.5
Step 3: Find Q1:
Q1 is the median of the lower half of the data set, which includes the values from the 1st to the median (excluding the median itself).
Lower half: 37, 45, 69, 74
Median of lower half = (45 + 69) / 2 = 57
Step 4: Find Q3:
Q3 is the median of the upper half of the data set, which includes the values from the median to the last value.
Upper half: 82, 89, 99, 100
Median of upper half = (89 + 99) / 2 = 94
Step 5: Calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 94 - 57 = 37
Therefore, the interquartile range of the test scores is 37.