Question 21·Hard·One-Variable Data Distributions; Measures of Center and Spread
A survey was given to residents of all 50 states asking whether they had earned a bachelor’s degree or higher. The results from 7 of the states are shown.
| State | Percent of residents |
|---|---|
| A | 21.9% |
| B | 27.9% |
| C | 25.9% |
| D | 19.5% |
| E | 30.1% |
| F | 36.4% |
| G | 35.5% |
The median percent of residents who earned a bachelor’s degree or higher for all 50 states was 26.95%.
What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7 states and the median for all 50 states?
For median questions with a small list of numbers, always start by writing the data in order from smallest to largest. If there is an odd number of values, the median is the single middle value; if there is an even number, it is the average of the two middle values. Once you have the median you need, carefully compute the difference requested (often the absolute difference) and compare it directly to the answer choices, watching out for common mix-ups between mean and median.
Hints
Recall how to find a median
Think about what you do differently to find the median when there is an odd number of data points versus an even number.
Organize the data first
Before you look for the median of the 7 states, rewrite the percentages in increasing numerical order.
Compare the two medians
Once you know the median for the 7 states, subtract it from 26.95% (or vice versa) and focus on the positive difference in percent.
Desmos Guide
Use Desmos to find the median of the 7 states
In Desmos, type median([21.9, 27.9, 25.9, 19.5, 30.1, 36.4, 35.5]). Desmos will display the median value of these 7 numbers.
Find the difference between the two medians
In a new expression line, type abs(median([21.9, 27.9, 25.9, 19.5, 30.1, 36.4, 35.5]) - 26.95). The number Desmos outputs is the percent difference between the two medians; match this value to the closest answer choice.
Step-by-step Explanation
Put the 7 percentages in order
List the given percentages from smallest to largest:
19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4.
This ordered list will let you easily identify the median for these 7 states.
Find the median of the 7 states
There are 7 data values, so the median is the middle (4th) value in the ordered list.
- The ordered values are: 19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4.
- The 4th value is 27.9.
So, the median percent for these 7 states is 27.9%.
Compute the difference between the two medians
The median for all 50 states is 26.95%. The median for the 7 states is 27.9%.
Find the (absolute) difference:
So the difference between the two medians is 0.95%, which corresponds to choice B) 0.95%.