The table shows the distribution of the number of hours per day spent in studying...
MATHEMATICS
WAEC 2021
The table shows the distribution of the number of hours per day spent in studying by 50 students.
Number of hours per day | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
Number of students | 5 | 7 | 5 | 9 | 12 | 4 | 3 | 5 |
Calculate, correct to two decimal places,
the: (a) mean; (b) standard deviation.
Explanation
| x | f | fx | fx\(^2\) |
| 4 | 5 | 20 | 80 |
| 5 | 7 | 35 | 175 |
| 6 | 5 | 30 | 180 |
| 7 | 9 | 63 | 441 |
| 8 | 12 | 96 | 768 |
| 9 | 4 | 36 | 324 |
| 10 | 3 | 30 | 300 |
| 11 | 5 | 55 | 605 |
| £f = 50 | £fx = 365 | £fx\(^2\) = 2,873 |
(a) Mean(\(\overline{x}\)) = \(\frac{365}{50}\) = 7.30 (2 d.p.)
(b) Standard deviation = √(\(\frac{2873}{50}\)) - (7.3)\(^2\)
= √4.17
= 2.0421
= 2.04 (2 d.p.)
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