Question 28·Easy·One-Variable Data Distributions; Measures of Center and Spread
The table shows the number of hours each of 8 employees worked at a café last Saturday.
| Employee | Hours worked |
|---|---|
| A | 5 |
| B | 6 |
| C | 7 |
| D | 5 |
| E | 8 |
| F | 9 |
| G | 6 |
| H | 4 |
What is the median number of hours worked by these employees?
For median questions with a small data set, first rewrite all values in order from least to greatest—this reduces mistakes. Quickly count how many data points there are: if the number is odd, pick the single middle value; if it is even, average the two central values. Always double-check that you used the ordered list (not the original list) and that you chose the correct positions before matching your result to an answer choice.
Hints
Think about what median means
Median is not the same as the mean (average). It is the middle value when the numbers are placed in order from smallest to largest.
Reorder the data
Write the 8 hours worked in increasing order. This will help you clearly see which values are in the middle.
Handle an even number of data points
Since there are 8 employees (an even number), the median will be halfway between the two middle values in your ordered list. Identify those two middle values and then find their average.
Desmos Guide
Enter and sort the data
In Desmos, type sort([5,6,7,5,8,9,6,4]). Desmos will display the values in increasing order as a list.
Locate the middle two values
Count how many numbers are in the sorted list (you should see 8). Identify the 4th and 5th numbers in that list; those are the two middle values.
Calculate the median in Desmos
In a new Desmos line, type median([5,6,7,5,8,9,6,4]) or manually compute the average of the 4th and 5th values using (value4 + value5)/2. The result that Desmos outputs is the median number of hours.
Step-by-step Explanation
Recall what median means
The median of a data set is the middle value when the numbers are arranged in order.
- If there is an odd number of data points, the median is the single middle value.
- If there is an even number of data points, the median is the average of the two middle values.
List the data and put it in order
Write down the hours worked by the 8 employees:
- .
Now rearrange these from least to greatest:
- .
Identify the middle positions for an even number of values
There are 8 values in the ordered list. When there are 8 values, the middle is between the 4th and 5th values.
Count from the left:
- 1st:
- 2nd:
- 3rd:
- 4th:
- 5th:
- 6th:
- 7th:
- 8th:
So the two middle numbers are the 4th and 5th values, which are both .
Compute the median from the two middle values
For an even number of data points, the median is the average of the two middle values.
The two middle values are and , so the median is
Therefore, the median number of hours worked by these employees is 6.