Question 527·Medium·Math

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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?

Your answer

A request for the median of an unordered list means you need the middle after sorting, not the total divided by the count. With an even number of measurements, average the two middle values. Enter the measurements as a Desmos list and use $\operatorname{median}$ ; picking the middle entries in the original order can give a different result.

Hints

Hint 1
The median depends on position after sorting, not on which numbers happen to appear in the middle of the written list. With eight saplings, will there be one middle height or two?
Hint 2
An even count has two middle positions: for eight heights, they’re the fourth and fifth. Name the heights as a Desmos list, then use $\operatorname{median}$ to sort them and average that pair.

Step-by-step

Use a Desmos list to find the median
Step 1
Identify the middle positions
A median is the middle of the data after sorting. With $8$ saplings, the middle lies between the fourth and fifth heights, so you must average both. The middle entries as originally written aren't necessarily the median's middle values. Here, those entries are $48$ and $41$ , but the list isn't in order.
Step 2
Enter every height
Type $a=[42,39,44,48,41,47,40,66]$ to make a list named $a$ . Desmos displays the values stored in it. Check that all eight heights, including $66$ , are there.
Step 3
Read the median
Type $\operatorname{median}(a)$ . Desmos shows $43$ . To see why, the heights in order are $39,40,41,42,44,47,48,66$ , so the fourth and fifth are $42$ and $44$ ; their average is $43$ . The median sapling height is $43$ centimeters. Grid in 43.

Question 527·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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