Data sets can be explained through a variety of measures, most commonly by mean, median, and mode. Another important measure to know is range, or the difference between the largest and the smallest number in the set. This can show if the data is clustered or if there is an outlier. The interquartile range can be found by subtracting the median of the first quartile from the third quartile. Quartiles are identified by the numbers before and after the median of the full set of data. The smaller numbers are Q1, or the first quartile, and the larger numbers are Q3, or the third quartile.
Example: In the data set, find the range and the interquartile range.
Data Set: 43, 52, 24, 35, 83, 57
Arrange in numerical order: 24, 35, 43, 52, 57, 83
Find the range: 83 – 24 = 49
Find the interquartile range:
- Find the median: (43 + 52) / 2 = 95 / 2 = 47.5
- Q1 is 24, 35, 43 and Q3 is 52, 57, 83
- The median of Q1 is 35 and Q3 is 57
- To find the range, subtract: 57 – 35 = 22
On the test, the problems will be more complex but use the same XX. Here is an example of something similar to what can be expected on the test.
Data set: 65, 85, 90, 75, 95, 100, 100, 70, x
Given the data set, identify the value of x. The median of the data is 85 and the interquartile range is 25.
Arrange the data in numerical order: 65, 70, 75, 85, 90, 95, 100, 100, x
The value of x must be less than 85 to satisfy the median requirement.
The Q3 is 97.5 which makes the Q1 72.5, since the interquartile range is 25.
The median of 72.5 comes from the average of 70 and 75 since it is an even set of numbers. Therefore, the value of x must be either 70 or 75.
Consider the answer choices on the exam and choose the correct one. Note, both 70 and 75 would not be choices and only one option should exist.