The ages of 45 people at a concert are grouped as shown. Find the modal class and the mode.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The ages of people at a concert are grouped as shown.
| Age (years) | People |
|---|---|
| 10-20 | 6 |
| 20-30 | 11 |
| 30-40 | 15 |
| 40-50 | 9 |
| 50-60 | 4 |
Find the modal class and the mode.
Need a reminder? The key ideaShow
The modal class has the greatest frequency. For equal class widths,
where is the frequency before the modal class and the frequency after it. A missing neighbour has frequency . For inclusive classes use the boundaries.
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.
Given. The greatest frequency is , so the modal class is to years.
Plan. Use , , , and .
Step 1. The top. .
Step 2. The bottom. .
Step 3. The mode. years.
Answer: the modal class is to years and the mode is years.
Check. The mode lies inside the modal class. It is below the class mark , because the class before () is bigger than the class after ().
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