The table shows the distribution of masks obtained by students in an examination. Marks 50
FURTHER MATHEMATICS
WAEC 2019
The table shows the distribution of masks obtained by students in an examination.
| Marks | 50 - 54 | 55 - 59 | 60 - 64 | 65 - 69 | 70 - 74 | 75 - 79 | 80 - 84 | 85 - 89 |
| Frequency | 5 | 15 | 20 | 28 | 12 | 9 | 7 | 4 |
Using an assumed mean of 67, calculate, correct to one decimal place. the
a) Mean
b) Standard deviation of the distribution
Explanation
| x | f | d | fd | \(\delta\) | f\(\delta\) |
| 52 | 5 | -15 | -75 | 225 | 1125 |
| 57 | 15 | -10 | -150 | 100 | 1500 |
| 62 | 20 | -5 | -100 | 25 | 500 |
| 67 | 28 | 0 | 0 | 0 | 0 |
| 72 | 12 | 5 | 60 | 25 | 300 |
| 77 | 9 | 10 | 90 | 100 | 900 |
| 82 | 7 | 15 | 105 | 225 | 1575 |
| 87 | 4 | 20 | 80 | 400 | 1600 |
| Total | 100 | 10 | 7500 |
(a) To find mean; = 67 + \(\frac{10}{100}\) = 67.1
(b) Substitute and find the standard deviation as \(\sqrt{\frac{7500}{100} - (\frac{10}{100})^2}\) = \(\sqrt{74.99}\)
= 8.6597
= 8.7, correct to one decimal place
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *