Chapter 3

Problems SolvedLocation of Measures

:Data Describing

Problem 3-3

a.

XX

n

X

5 9 4 104

284

7

Problem 3-3

b.

03322

710747975

xx

X 13 13 12 15 7 15 5 12 6 7 12 10 9 13 12 161 x =

.statistics simple a isX b.

hourstimeover73.1015161

nXX a.

1.

Problem 3-10

Problem 3-14

50.1$5075

503540

5050.31000.140

WWx

x

41,15,39,54,31,15,33

15,15,31,33,39,41,54Mode = 15 and Median = 33

32.577

2287

33153154391541nX

X

Problem 3-18

12,8,17,6,11,14,8,17,10,8

6,8,8,8,10,11,12,14,17,17Mode = 8 and Median =10.5

11.110111

108101781411617812

nX

X

Problem 3-20

Problem 3.37x x(in an array)

28 24 28 – 38 = - 10 1032 28 32 – 38 = - 6 624 32 24 – 38 = - 14 1446 32 46 – 38 = + 8 844 38 44 – 38 = + 6 640 40 40 – 38 = + 2 254 42 54 – 38 = + 16 1638 44 38 – 38 = 0 032 46 32 – 38 = - 6 642 54 42 – 38 = + 4 4

x = 380 x = 380 = 0 = 72

)X(X |XX|

|XX| Σ)X(X ΣΣ Σ

392

4038Median

Problem 3.37 Continued

302454. LowHighRangea

3810380.

nx

xb

2.71072

n

xxMDc.

%93.2310038092.9100..

32996.092.9

393833

XSVC

SMEDIANXS k4.Chtorefer

098.2

4.4522

5125

5147

25625

5147

525

5147 2

2

2543738

x

x

147

169

499

64

2

2

x

x

Nx

Nx2

2

Problem 3.37b – Computational Method

5.0525

nxμ

222μ)(x0μ)(x114423427423938μxμxx 2

Problem 3.41

098.24.4

4.45222

22

Nx

Problem 3.41 Continued

3438.624.40

24.40520.201

16.1084.1014056.114.313376.576.7122

56.26.112816.216.4125

.

600,129$6.1295

6485

140133122128125.

000,18000,122000,140Range.

22

20.2012

0.0648

2

Nx

xxxc

orNX

b

a

xxx

Problem 3.46

...

IndustriesTMVtheofsalariestheindispersionlessisThereclosearecompaniesofMeansd

3438.6

24.405

2.2015

8.31680318825

539831882

222

2

N

NX

X

Problem 3.46 (Cont.)Alternative Solution using

Computational Method

4520

22020

1143342422424664242293477

2

2

n

xx

xxxxx

xxxxx

Problem 3.47a

x

2x 7 4 9 2 4 6 3 6 2 4

3 9

20x 1022x

3.47b

5.5

345.2

422

1522

1

2

2

S

nxx

s

3.47c Standard Deviation

5.5

345.24

8010215520102

1

2

2

22

s

s

nnx

xs

3.47d Standard Deviation

X28 10032 3624 19646 6444 3640 454 25638 032 3642 16

X = 380 = 744 9.092S82.6667S

82.6667110744S

1nXX

S

2

22

Problem 3-49 (see problem 3-37)

2)X(X

2)X(XΣΣ

%6969.8.11111 22 or

k

Problem 3.53

%8484.5.211

11

..5.240

500600..5.240

50040040500

2

2

or

k

devsstddevsstd

sx

Problem 3.54

Class f M fM ( ) ( )2 f( )2

20<30 7 25 175 -22.287 496.71 3476.97

30<40 12 35 420 -12.287 150.97 1811.64

40<50 21 45 945 -2.287 5.23 109.84

50<60 18 55 990 7.713 59.49 1070.82

60<70 12 65 780 17.713 313.75 3765.00

f = n = 70        fM = 3310 f( )2= 10234.27Σ Σ XM

XMXM XM

Problem 3-59

Σ

25.76%10047.28712.179100

xsCV

12.179148.32S

32.14817027.10234

1n

2X-MfΣ2Sb.

47.287703310

nfMΣXa.

Problem 3-59 cont’d

Age f M fM ( ) ( )2 f( )2

10<20 3 15 45 -25.17 633.53 1900.59

20<30 7 25 175 -15.17 230.13 1610.91

30<40 18 35 630 -5.17 26.73 481.14

40<50 20 45 900 4.83 23.33 466.58

50<60 12 55 660 14.83 219.93 2639.15

n=60        fM = 2410 f( )2= 7098.37Σ Σ

40.17602410

nfMX

10.968120.3111)(60

7098.371)(n

2)X-f(MS

XM

XMXM XM

Problem 3-60

27.30%10040.17

10.968100xsCV

Problem 3-65

5.372

3837

52,46,46,43,42,41,39,38,37,34,32,30,30,18,12,5.

06.3416

5.....38304352.

Median

b

nx

xa