Question 49·Easy·One-Variable Data Distributions; Measures of Center and Spread
| Day | High temperature (°F) |
|---|---|
| Monday | 68 |
| Tuesday | 71 |
| Wednesday | 75 |
| Thursday | 70 |
| Friday | 69 |
| Saturday | 75 |
| Sunday | 72 |
Based on the temperatures recorded during the week shown in the table, what is the median high temperature, in degrees Fahrenheit?
For median questions, always write the data values in order from least to greatest first. Then count how many values there are: if the number of data points is odd, the median is the single middle value; if it’s even, the median is the average of the two middle values. Avoid using the original table order or confusing the median with the mean (average).
Hints
Understand the term
Think about what the median of a data set represents in statistics. Is it the average, the middle value, or something else?
Reorder the data
Before you choose the median, make sure the temperatures are written in order from least to greatest. Do not just pick a number from the original table order.
Use the number of data points
Count how many temperatures there are in the week, and then figure out which position in the ordered list will be the median.
Desmos Guide
Use Desmos to compute the median
In a new expression line, type median(68,71,75,70,69,75,72) and press Enter. The value that Desmos outputs is the median of these seven temperatures.
Step-by-step Explanation
Recall what “median” means
The median of a set of numbers is the middle value when the numbers are arranged in order from least to greatest. With 7 numbers, the median will be the 4th number in the ordered list, because 3 numbers will be below it and 3 numbers will be above it.
List and sort the temperatures
Write the temperatures from the table as a list:
68, 71, 75, 70, 69, 75, 72
Now sort them from least to greatest:
68, 69, 70, 71, 72, 75, 75
Find the middle value in the ordered list
There are 7 values, so the median is the 4th value in the ordered list.
Count to the 4th number: 1st = 68, 2nd = 69, 3rd = 70, 4th = 71, 5th = 72, 6th = 75, 7th = 75.
So, the median high temperature is 71 degrees Fahrenheit.