Further Mathematics 2, Nov/Dec. 2014

Further Mathematics Paper 2, Nov/Dec. 2014

Questions:	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	Main

General Comments
Weakness/Remedies
Strength

Question 12

The table shows the frequency distribution of the ages of workers in a factory.

Ages (years)

Number of workers

15 – 19
20 – 24
25 – 29
30 – 34
35 – 39
40 – 44
45 – 49
50 – 54
55 – 59
60 - 64

5
22
30
32
25
36
32
30
21
2

Using an assumed mean of 42, calculate, correct to one decimal place, the:

mean;

variance

of the distribution

_____________________________________________________________________________________________________

Observation

This question was reported to be very popular among the candidates and their performance was commended. However, it was also observed that some candidates did not use the assumed mean as demanded by the rubrics of the paper.

Candidates were expected to obtain the following table.

Ages	F	X	d	fd	d2	fd2
15 - 19	5	17	-25	-125	625	3125
20 - 24	22	22	-20	-440	400	8800
25 - 29	30	27	-15	-450	225	6750
30 - 34	32	32	-10	-320	100	3200
35 - 39	25	37	-5	-125	25	625
40 - 44	36	42	0	0	0	0
45 - 49	32	47	5	160	25	800
50 - 54	30	52	10	300	100	3000
55 - 59	21	57	15	315	225	4725
60- 64	2	62	20	40	400	800
	∑f = 235			∑fd = -645		∑fd2 = 31825

Using the table, the mean was calculated using the formula, mean = A + , where A = Assumed mean = 42 i.e. Mean = 42 - = 42 – 2.74 = 39.26
Variance was obtained by applying the formula – = – ( = 127.89.