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.)