Median Statistics Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
mediumThe ordered data set is 4, 7, 8, 9, 12, 14, 18. What is the median, and if 30 is added to the set, does the median change?
Solution
- 1 Step 1: With 7 values, the middle value is the 4th value, so the median is .
- 2 Step 2: Adding 30 creates 8 values: 4, 7, 8, 9, 12, 14, 18, 30. The new median is , so it does change.
Answer
The original median is . After adding 30, the median becomes , so yes, it changes.
The median depends on the position of the middle value or values in the ordered list. Adding one extra value can change whether the set has an odd or even number of data points, which may change the median.
About Median
The median is the middle value when all data points are arranged in order from smallest to largest. Half the values lie above it and half below. For an even number of values, the median is the average of the two middle values.
Learn more about Median →