waecE-LEARNING
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

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

 

  1. mean;
  1. 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.

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