The frequency distribution shows tha marks of 100 students in a Mathematics test.
| Marks | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 | 81-90 | 91-100 |
|
No. of Students |
2 | 4 | 9 | 13 | 18 | 32 | 13 | 5 | 3 | 1 |
(a) Draw cumulative frequency curve for the distribution .
(b) Use your curve to estimate : (i) the median ; (ii) the lower quartile ; (iii) the 60th percentile.
Explanation
(a)
| Marks | Frequency | Cum. freq |
| 1 - 10 | 2 | 2 |
| 11 - 20 | 4 | 6 |
| 21 - 30 | 9 | 15 |
| 31 - 40 | 13 | 28 |
| 41 - 50 | 18 | 46 |
| 51 - 60 | 32 | 78 |
| 61 - 70 | 13 | 91 |
| 71 - 80 | 5 | 96 |
| 81 - 90 | 3 | 99 |
| 91 - 100 | 1 | 100 |
(b)(i) \(N = \sum f = 100\)
\(Median = \frac{1}{2}N = \frac{1}{2}(100)\)
= 50th percentile.
\(\therefore Median = 52\).
(ii) \(Q_{1} = \frac{1}{4} N = \frac{1}{4}(100)\)
= 25th percentile.
\(\therefore Q_{1} = 39\)
(iii) 60th percentile = 55.