Question 5·Medium·One-Variable Data Distributions; Measures of Center and Spread
Melissa recorded the price of one gallon of regular gas at five local stations.
| Station | Price (USD) |
|---|---|
| 1 | $3.699 |
| 2 | $3.609 |
| 3 | $3.729 |
| 4 | $3.679 |
| 5 | $3.729 |
What is the median of the gas prices Melissa recorded?
For median questions with a small list of values, first count how many data points you have. Then rewrite the values in order from least to greatest. If the count is odd, the median is the single middle value; if it’s even, take the average of the two middle values. Always double-check that you are using the correct rule (odd vs. even number of values) to avoid averaging when you don’t need to.
Hints
Think about what "median" means
The median is not the smallest, largest, or the average of all the numbers. It is the middle value when the numbers are put in order.
Put the prices in order
Write all five gas prices from least to greatest. This will make it easy to see which one is in the middle.
Use the fact that there are 5 prices
When there are 5 values, the median is the 3rd value in the ordered list. Once you have them in order, count to find the 3rd price.
Avoid a common mistake
Do not average two prices here—averaging the middle two is only for when there is an even number of data points, not an odd number like 5.
Desmos Guide
Use Desmos to compute the median directly
In Desmos, type:
median({3.699, 3.609, 3.729, 3.679, 3.729})
Desmos will output a single number; that result is the median of the gas prices and should match one of the answer choices.
Step-by-step Explanation
Recall what the median means
The median of a set of numbers is the middle value after the numbers are arranged in order from least to greatest.
- If there are an odd number of values (like 5), the median is the one number in the middle.
- If there are an even number of values, the median is the average of the two middle numbers.
List the gas prices and count them
The prices given are:
- Station 1: $3.699
- Station 2: $3.609
- Station 3: $3.729
- Station 4: $3.679
- Station 5: $3.729
There are 5 prices in total, so the median will be the 3rd value once the prices are ordered from least to greatest.
Order the prices from least to greatest
Arrange the five prices in increasing order:
- $3.609
- $3.679
- $3.699
- $3.729
- $3.729
Now, identify the 3rd number in this ordered list, since that is the middle value when there are 5 numbers.
Identify the median and match it to an answer choice
From the ordered list
- 1st: $3.609
- 2nd: $3.679
- 3rd: $3.699
- 4th: $3.729
- 5th: $3.729
The 3rd (middle) value is $3.699, so the median gas price is $3.699, which corresponds to choice C.