The histogram above represents the scores of some candidates in an examination.
(a) Using the histogram, construct a frequency distribution table indicating clearly the class intervals ;
(b) Draw a cumulative frequency curve of the distribution and use it to estimate the :
(i) median ; (ii) quartile deviation.
Explanation
(a)
Score | Freq |
9 – 18 | 4 |
19 – 28 | 6 |
29 – 38 | 8 |
39 – 48 | 13 |
49 – 58 | 15 |
59 – 68 | 10 |
69 – 78 | 3 |
79 – 88 | 1 |
(b)
Upper class boundary |
Freq. | Cum. Freq |
18.5 | 4 | 4 |
28.5 | 6 | 10 |
38.5 | 8 | 18 |
48.5 | 13 | 31 |
58.5 | 15 | 46 |
68.5 | 10 | 56 |
78.5 | 3 | 59 |
88.5 | 1 | 60 |
(i) Median, (Q_{2} = frac{1}{2} text{Nth score})
= (frac{1}{2} text{60th score} = 30th) score.
= (48.4)
(ii) (Q_{1} = 35.5 ; Q_{3} = 57.5)
Quartile deviation = (frac{1}{2} (Q_{3} – Q_{1}))
= (frac{1}{2} (57.5 – 35.5) = frac{1}{2} (22))
= (11.0)