Question 43·Easy·One-Variable Data Distributions; Measures of Center and Spread
The table shows the number of postcards Amy mailed on each of 9 consecutive days.
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Postcards mailed | 3 | 5 | 2 | 4 | 6 | 5 | 2 | 3 | 5 |
What is the median number of postcards Amy mailed per day during this 9-day period?
For median questions, first rewrite the data in order from least to greatest—this is essential. Count how many data points there are: if it’s an odd number, the median is the value at position in the ordered list; if it’s even, it’s the average of the two middle values. Avoid shortcuts like eyeballing or picking the most frequent number, and double-check your counting of positions to prevent simple mistakes.
Hints
Focus on the definition of median
The median is not the average; it is the middle value when the data are arranged in numerical order.
Put the data in order
Write the nine postcard counts from smallest to largest before you try to find the median.
Use the fact there are 9 days
With 9 data values, how do you determine which position in the ordered list is the median?
Desmos Guide
Enter the data as a list
In Desmos, type the list of postcard counts as [3,5,2,4,6,5,2,3,5].
Use Desmos to compute the median
On a new line, type median([3,5,2,4,6,5,2,3,5]). The value that Desmos returns is the median number of postcards per day.
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 from least to greatest. For an odd number of data points, the median is the single value right in the middle.
List the data in order
The numbers of postcards mailed are:
Reorder these from least to greatest:
Find the middle (5th) value
There are 9 values total, so the median is the 5th value in the ordered list (because ).
Counting in the ordered list , the 5th value is 4.
So, the median number of postcards Amy mailed per day is 4.