Measures of Central Tendency
Calculations with the Mean
This section considers calculations concerned with the mean, which is often taken to be the most important measure of the average of a set of data but this depends on the context.
Worked Examples
1
The mean of a sample of 6 numbers is 3.2. An extra value of 3.9 is included in the sample. What is the new mean?
Show me
| Total of original numbers | = 6 × 3.2 |
| = 19.2 | |
| New total | = 19.2 + 3.9 |
| = 23.1 | |
| New mean | = |
| = 3.3 |
2
The mean number of a set of 5 numbers is 12.7. What extra number must be added to bring the mean up to 13.1?
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| Total of the original numbers | = 5 × 12.7 |
| = 63.5 | |
| Total of the new numbers | = 6 × 13.1 |
| = 78.6 | |
| Difference | = 78.6 − 63.5 |
| = 15.1 |
So the extra number is 15.1.
3
Rohan's mean score in three cricket matches was 55 runs.
(a)
How many runs did he score altogether?
Show meMean = 55 =
so total scored = 3 × 55 = 165
After four matches his mean score was 61 runs.
(b)
How many runs did he score in the fourth match?
Show meTotal scored = 4 × 61 = 244
| Fourth match score | = 244 − 165 |
| = 79 |
Exercises
