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A coaching centre grouped the scores of 50 students in a practice test, out of 100…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A coaching centre grouped the scores of students in a practice test, out of . The centre wants a measure of spread that can be compared with the one from last year, when the test was out of . For that, the centre will use the coefficient of mean deviation about the mean, which has no unit.
| Score | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
|---|---|---|---|---|---|
| Students | 6 | 9 | 15 | 12 | 8 |
Find the mean score, the mean deviation about the mean, and the coefficient of mean deviation. Take the class marks as and .
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The worked solution
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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 mean. . So marks.
Step 2. The distances. The class marks are and away from the mean.
Step 3. Multiply by the frequencies. , then , , and . The sum is .
Step 4. The mean deviation. marks.
Step 5. The coefficient. .
Answer: mean marks, mean deviation marks and coefficient .
What if? If last year's test had a coefficient of , this year's marks are more spread out compared with their mean. The coefficient has no unit, so it can be compared even though the two tests had different total marks.
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