The frequency distribution shows tha marks of…

Question 1 Report

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.

Answer

Answer Details

(a) Less-than cumulative frequency table

Marks	Class boundary	Frequency	Cumulative frequency
1–10	10.5	2	2
11–20	20.5	4	6
21–30	30.5	9	15
31–40	40.5	13	28
41–50	50.5	18	46
51–60	60.5	32	78
61–70	70.5	13	91
71–80	80.5	5	96
81–90	90.5	3	99
91–100	100.5	1	100

Plot cumulative frequency against the upper class boundaries, beginning with 0.5,0 . Draw a smooth increasing curve through the plotted points.

(b) Estimates from the ogive

The total frequency is 0.5+99.5=100 students.

Median position =rac{100}{2}=50 . From cumulative frequency 50, the corresponding mark is approximately 52 marks.
Lower quartile position =rac{100}{4}=25 . From cumulative frequency 25, the corresponding mark is approximately 39 marks.
60th percentile position =rac{60}{100} imes100=60 . From cumulative frequency 60, the corresponding mark is approximately 55 marks.

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 S...