Question 17·Medium·One-Variable Data Distributions; Measures of Center and Spread
A botanist records the heights, in centimeters, of 8 saplings:
42, 39, 44, 48, 41, 47, 40, 66
What is the median height, in centimeters, of these saplings?
For median questions, always first sort the data from smallest to largest. Then quickly count how many values there are: if the count is odd, pick the single middle value; if it is even, average the two central values. Be especially careful not to confuse the median with the mean or with the average of the smallest and largest numbers.
Hints
Start by organizing the data
The numbers are not in order yet. Rewrite the heights from smallest to largest before you try to find the median.
Think about the number of data points
Count how many heights there are. Is that number odd or even? How does that affect how you find the median?
Identify and combine the middle values
Once the list is ordered, locate the 4th and 5th values. What calculation do you perform with these two numbers to get the median?
Desmos Guide
Use Desmos to compute the median directly
In a Desmos expression line, type median({42,39,44,48,41,47,40,66}). The value that Desmos outputs for this expression is the median height of the saplings.
Step-by-step Explanation
Put the data in order from least to greatest
The original heights are:
42, 39, 44, 48, 41, 47, 40, 66
First, rewrite them in increasing order:
39, 40, 41, 42, 44, 47, 48, 66
Decide which positions give the median
There are 8 data values.
- When the number of values is odd, the median is the single middle number.
- When the number of values is even (like 8), the median is the average of the two middle numbers.
With 8 values, the two middle positions are the 4th and 5th values in the ordered list.
From the ordered list:
- 4th value is 42
- 5th value is 44
Find the average of the two middle values
To get the median, find the average of 42 and 44:
So, the median height of the saplings is 43 centimeters.