Question 29·Medium·One-Variable Data Distributions; Measures of Center and Spread
A technology reviewer measured the battery life (in hours) of eight newly released smartphones during continuous video playback.
| Phone | Battery life (hours) |
|---|---|
| A | 7.3 |
| B | 8.1 |
| C | 8.6 |
| D | 7.9 |
| E | 9.0 |
| F | 8.4 |
| G | 8.4 |
| H | 8.8 |
What is the median battery life of the eight smartphones?
For median questions, always start by listing the data in order from least to greatest—never use the original order from the table. Then count how many data points there are: if the number is odd, the median is the single middle value; if it’s even, take the average of the two middle values (the n/2-th and (n/2 + 1)-th values in the ordered list). Be careful to use the correct positions and avoid accidentally using unsorted values or confusing the median with the mean.
Hints
Start by organizing the data
Write the 8 battery life values in order from least to greatest. The median is always found using the ordered list, not the original order from the table.
Think about how many values there are
Count the number of smartphones. Is it an odd or even number? The rule for finding the median is slightly different in each case.
Use the correct rule for an even number of data points
When there is an even number of data values, the median is the average of the two middle values in the ordered list. Identify those two values, then find their average.
Desmos Guide
Use Desmos to verify the median calculation
In Desmos, type the average of the two middle values from the ordered list as a single expression, like (8.4 + 8.4) / 2. Then look at the numeric result Desmos gives you; that value is the median battery life.
Step-by-step Explanation
List the battery lives and sort them
Write down all the battery life values from the table:
Now put them in order from least to greatest:
Identify which positions determine the median
Count how many data values there are. There are 8 smartphones, so there are 8 battery life values.
For an even number of values (like 8), the median is not just one middle value. Instead, it is the average of the two middle values.
In a list of 8 ordered values, the middle two are the 4th and 5th values in the list.
Average the two middle values to get the median
From the ordered list
the 4th and 5th values are both .
Compute their average:
So, the median battery life is hours, which corresponds to answer choice C.