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.