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A club has 50 members of ages from 20 to 50 years…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A club has members of ages from to years.
| Age (years) | Members |
|---|---|
| 20-25 | 3 |
| 25-30 | 9 |
| 30-35 | 15 |
| 35-40 | 12 |
| 40-45 | 7 |
| 45-50 | 4 |
The less than curve and the more than curve are drawn on one graph. At what height do they cross, and what age is read at the crossing?
Need a reminder? The key ideaShow
The less than cumulative frequency of a limit counts the values below it and is plotted at the upper limit. The more than cumulative frequency counts the values above it and is plotted at the lower limit. At every limit, less than plus more than equals . The curves cross at the height , and the horizontal reading is the median.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The height. At the crossing both totals are equal, and they add up to . So each is . The height is .
Step 2. The class. The less than total is at years and at years. So the height lies in the class to .
Step 3. The reading. , , and . The age is years.
Answer: the curves cross at the height , and the age read there is years, the median.
Check. The more than total at years is .
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