Dylan is going fishing. The lengths, in centimeters, of nine earthworms are shown below. He just caught a tenth earthworm that is 9.5 centimeters long. What is the median of the data once the tenth earthworm is included in the data set?
3, 4, 5, 5, 6, 7, 8, 9, 10
®
{x
A
6
{x
B
6.65
4x
C
9.5
E
D
6.5
Next
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To find the median, we need to first put the data in order from least to greatest:
3, 4, 5, 5, 6, 7, 8, 9, 10, 9.5
Now we can determine the middle number(s). Since there are an odd number of data points, the median is simply the middle number:
Median = 6
Therefore, the answer is (A) 6.
To find the new median once the tenth earthworm is included in the data set, follow these steps:
1. Arrange the data in ascending order: 3, 4, 5, 5, 6, 7, 8, 9, 10, 9.5
2. Count the number of data points, which is 10.
3. Since the number of data points is even, find the average of the two middle numbers.
The two middle numbers are the 5th and 6th numbers: 6 and 7.
Average = (6 + 7) / 2 = 6.5
Therefore, the median of the data set, once the tenth earthworm is included, is 6.5. So the answer is option D.