Question 52·Easy·One-Variable Data Distributions; Measures of Center and Spread
The daily high temperatures (in degrees Fahrenheit) recorded in a certain city for 9 consecutive days are shown in the table below.
| Day | Temperature (°F) |
|---|---|
| 1 | 72 |
| 2 | 68 |
| 3 | 70 |
| 4 | 75 |
| 5 | 71 |
| 6 | 69 |
| 7 | 74 |
| 8 | 68 |
| 9 | 70 |
What is the median of the daily high temperatures for these 9 days?
For SAT questions asking for the median, always first rewrite the data in ascending order, then count how many data points there are. If the count is odd, the median is the value at position in the ordered list; if it is even, average the two middle values. Be careful not to confuse the median with the mean (average) and avoid grabbing a "middle-looking" value from the original, unordered data.
Hints
Focus on the definition of median
Ask yourself: what does median mean in statistics? It is not the same as the mean (average). You are looking for the middle value of an ordered list.
Reorder the data
Write all 9 temperatures in a list from smallest to largest. This step is essential before trying to find the median.
Use the number of data points
There are 9 temperatures. For an odd number of data points, the median is the value in the exact middle position. Which position number is in the middle of 1 through 9?
Locate the middle value
Once you know which position is the middle one, count that far into your ordered list and read off the temperature at that position.
Desmos Guide
Enter the temperature data as a list
In a Desmos expression line, type T = [72, 68, 70, 75, 71, 69, 74, 68, 70] to store all the temperatures in a list named T.
Check the ordered list and find the median
On the next line, type sort(T) to see the temperatures in order from least to greatest. Then, on a new line, type median(T). The value Desmos shows for median(T) is the median of the daily high temperatures.
Step-by-step Explanation
Recall what the median means
The median of a data set is the middle value when all the numbers are arranged in order from least to greatest.
- If there is an odd number of data points, the median is the exact middle number.
- If there is an even number of data points, the median is the average of the two middle numbers.
Here, there are 9 days, so there are 9 data values (an odd number). You will be looking for the middle (5th) value once they are ordered.
List the temperatures in order
Start with the temperatures given:
72, 68, 70, 75, 71, 69, 74, 68, 70
Now arrange them from least to greatest:
68, 68, 69, 70, 70, 71, 72, 74, 75
Check that you still have 9 numbers and that none were left out or changed.
Find the position of the median
Since there are 9 data values, the median is the value in position
- middle position
So the 5th value in the ordered list is the median.
Identify the value at the middle position
Look at the ordered list:
68, 68, 69, 70, 70, 71, 72, 74, 75
Count to the 5th number:
1st → 68
2nd → 68
3rd → 69
4th → 70
5th → 70
The 5th value is 70, so the median temperature is 70°F, which corresponds to answer choice B) 70.