Question 31·Easy·One-Variable Data Distributions; Measures of Center and Spread
The table shows the number of pages Olivia read in her book each day for one week.
| Day | Pages read |
|---|---|
| Monday | 15 |
| Tuesday | 20 |
| Wednesday | 18 |
| Thursday | 22 |
| Friday | 20 |
| Saturday | 25 |
| Sunday | 19 |
What is the median number of pages Olivia read per day for that week?
For median questions, immediately write the data values as a simple list, then sort them from smallest to largest—never try to find the median from an unsorted table. Count how many data points there are: if the number is odd, the median is the single value at position ; if it’s even, it’s the average of the two middle values. To avoid mistakes under time pressure, you can also cross out the smallest and largest values in pairs until only the middle value (or middle two) remains.
Hints
Identify the data
Write down all the page counts from the table as a list of numbers without the day names.
Put the data in order
Rearrange the list of page counts so they go from the smallest number of pages to the largest number of pages.
Find the middle of an odd-sized list
There are 7 numbers. After ordering them, which position (1st, 2nd, 3rd, etc.) will be exactly in the middle?
Pick the value at the middle position
Once you know the middle position, look back at the ordered list and identify the value in that spot.
Desmos Guide
Enter the data as a list
In Desmos, type L = [15, 20, 18, 22, 20, 25, 19] to store the page counts in a list named L.
Use the median function
On the next line, type median(L) and look at the numerical result that Desmos displays; that value is the median of the data. Match that value to one of the answer choices.
Step-by-step Explanation
Recall what the median is
The median is the middle value of a data set after the values are arranged from smallest to largest. For an odd number of data points, the median is the single value that has the same number of data points on each side.
List the data from the table
Write down the number of pages Olivia read each day:
15, 20, 18, 22, 20, 25, 19
Put the numbers in order
Arrange the numbers from least to greatest:
15, 18, 19, 20, 20, 22, 25
Locate the middle value
There are 7 numbers, so the median is the value in position , which is the 4th number in the ordered list.
The 4th number is 20, so the median number of pages Olivia read per day that week is 20.