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2

67

12

)24(2

1Median

th

th

5.57

2

5857

6

)24(4

1Q1

th

th

74

18

)24(4

3Q3

th

th

1M

c.

75.32

)5.5774(2

35.57

)(2

3QboundaryLower 131

QQ

75.106

)5.5774(2

374

)(2

3QboundaryUpper 131

QQ

Outlier = 1081 M

2M

4a)

Interquartile range = 13 QQ

= 74 -57.5 = 16.5

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5. 2M

6 a) GraphYear Quarter Unemployed 4-quarter Centred 4-quarter Deviation

3M

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4

school

leavers

moving

average

moving average

(t)

(y-t)

2010 1 22

2 12

43.75

3 110 43.625 66.375

43.504 31 45.25 -14.250

47.00

2011 1 21 52.00 -31.000

57.00

2 26 61.875 -35.875

66.75

3 150 70.375 79.625

74.00

4 70 75.250 -5.250

76.50

2012 1 50 76.000 -26.000

75.50

2 36 80.500 -44.50085.50

3 146

4 110

b) seasonal variation

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4

2010 66.375 -14.250

2011 -31.000 -35.875 79.625 -5.250

2012 -26.000 -44.500

Unadjusted

seasonal

variation

-28.500 -40.188 73.000 -9.750

Correctionfactor

-1.3595 -1.3595 -1.3595 -1.3595

Seasonal

Variation

-27.14 -38.83 74.36 -8.39

C)The least square method

4822 x 66x 794182 y 784y 4627xy

12

)66(482

12)784)(66(4629

2

= 2.664 1M

[1M]

[2M]

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5

12

66664.2

12

784a =50.68

Regression line, y= 50.68+2.664x

For the first quarter of the year 2013,e

T = 50.68+2.664(13) = 85.312

Unemployed school leavers for the first quarter of the year 2013=85.312+ (-27.14) = 58.172 59

Or

Average quarterly increment =7

625.435.80 =5.2679

For the first quarter of the year 2013,e

T = 80.5 + 3 x 5.2679 = 96.304

Unemployed school leavers for the first quarter of the year 2013

= 96.304 + (-27.14)= 69.164 69

1M

1M

1M

1M

2M

1M

7a Histogram

b) 5.62)125(21

21 N

minutes58.30)1(30

45)125(2

1

30

2

1

Median,

cf

FN

LMm

2M

x f fx 2fx Cumulative

frequency,F26.5 6 6

28.5 12 18

29.5 27 45

30.5 30 75

31.5 18 93

32.5 14 107

33.5 9 116

34.5 4 120

37.5 5 125

5.3861fx 25.1199052 fx

89.30125

5.3861

,Mean

f

fx

x

220.2)89.30(125

25.119905,DeviationStandard 2

2

f

fx

f

fx

1M

2M

c. Pearson coefficient of skewness 1M

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6

=deviationstandard

median)3(mean= 4189.0

2.220

)58.303(30.89

The distribution is positively skewed or skewing to the right.

1M

7d)

.The number of times a bus arrives at town B between 0830 hours and 0836

hours = 122-45 = 77 2M

8a) Let X be the number of books read by an adult

Then, )5(0PX

a)

1404.0!3

)5()3(

35

e

XP

b) In 5 years, 2555 1M1M

1M

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7

0.1

!2

)25(

!1

)25(

!0

)25(-1

)]2()1()0([1)2(

225125025

eee

XPXPXPXP

1M

b)(i)

0.0228

0.9772-1

2)P(z-1

2)P(z

10

5070)70(

zPXP

Hence, percentage of candidates = 0.0228 x 100% = 2.28%(ii)

76.44

524.010

50

0.524z

0.70z)P(Z

70.010

50

70.0)(

x

x

xZP

xXP

Hence, minimum marks required = 45

2M

1M

2M

1M

8c) Expected number, 8)(E npx

Variance, Var (x) = npq = 1.6

8

6.1

np

npq

q = 0.2 p = 0.8 n = 10 )8.0,10(X (i) P( a teacher chosen at random owns a proton car) = 0.8(ii) P( exactly 4 teachers from the group own Proton cars)

= P(X = 4)

= 4104410 )2.0()8.0( C = 0.005505

2M

1M

2M