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A survey of 40 people gave this table of the minutes they spend online each day…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A survey of people gave this table of the minutes they spend online each day.
| Minutes | People |
|---|---|
| 10-20 | 4 |
| 20-30 | 10 |
| 30-40 | 16 |
| 40-50 | 7 |
| 50-60 | 3 |
The mean found from the class marks is the estimate. Now put every person at the lower end of their class. The mean found this way is the smallest the true mean can be. Put every person at the upper end of their class, and the mean found is the largest it can be.
Find the estimate, the smallest possible mean and the largest possible mean.
Need a reminder? The key ideaShow
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 estimate. . The sum is . The estimate is minutes.
Step 2. The smallest. With the lower ends, . The mean is minutes.
Step 3. The largest. With the upper ends, . The mean is minutes.
Answer: the estimate is minutes, and the true mean is between and minutes.
What do you notice? The smallest and the largest means differ by exactly minutes, the class width. The estimate lies in the middle of the two. So a table with narrower classes gives a narrower range for the true mean.
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