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MNS 601

Statistics for Business

Dr. Nittaya Wiboonprapat

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Data & Statistics

Dataare collections of any number of related

observations.

Statistics is a collection of methods for

planning studies and experiments, obtaining

data, and then organizing, summarizing,

presenting, analyzing, interpreting, and

drawing conclusions based on the data.

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Apopulation is the complete collection of all

elements (scores, people, measurements, and

so on) to be studied. The collection is

complete in the sense that it includes all

subjects to be studied.

A sample is a sub collection of members

selected from a population.

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Arranging data

Data Array: arranges values in ascending

or descending order

Frequency Distribution (or frequency

table): organizes data into classes

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Data Array

Arrange these data in a data array:

51 66 61 82 65 54 56 92

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Construct Frequency Distributions

Use these data to construct relative frequency distributions using 7 equal intervals.

83 51 66 61 82 65 54 56 92 60

65 87 68 64 51 70 75 66 74 68

44 55 78 69 98 67 82 77 79 62

38 88 76 99 84 47 60 42 66 74

91 71 83 80 68 65 51 56 73 55

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7 Intervals

Class Frequency Relative Frequency

30-39 1 0.02

40-49 3 0.06

50-59 8 0.16

60-69 16 0.32

70-79 10 0.20

80-89 8 0.16

90-99 4 0.08

50 1.00

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Measures of Central Tendency

Mean: Ungrouped Data

Grouped Data

Median: Ungrouped DataGrouped Data

Mode: Ungrouped Data

Grouped Data

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The Mean

Population X1, X2, , XN

m

Population Mean

N

X

N

1=i

im

Sample x1, x2, , xn

Sample Mean

n

x

x

n

1=i

i

x

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Mean: Ungrouped Data

x

xi

i1

n

nx1 x

2 ... x

n

n

Example: The salaries of 5 employees (in thousands) are 14, 17,21, 18, 15. Find the mean.

Solution: Sum = (14 + 17 + 21 + 18 + 15) = 85Number of numbers: 5

Divide 85 by 5 = 17. The average salary is $17,000

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Find the mean for

30.8, 31.7, 30.1, 31.6, 32.1

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26.315

5.156

5

1.326.311.307.318.30

55

54321

5

1xxxxx

x

xi

i

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Exercises

Page 79: Exercise 3-6

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Mean: Grouped Data

x

(f* x)n

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Mean: Grouped Data

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Mean: Grouped Data

Class Frequency

10

10.9 1

11 11.9 4

12 12.9 6

13 13.9 8

14

14.9 12

15 15.9 11

16 16.9 8

17 17.9 7

18

18.9 6

19 19.9 2

65

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Median: Ungrouped Data

The population or samplemedianis a value such that 50% of allmeasurements lie above (or below) it.The median Md is found as follows:

1. If the number of measurements is odd, the median is themiddlemost measurement in the ordered values.

2. If the number of measurements is even, the median is theaverage of the two middlemost measurements in the orderedvalues.

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Example: Sample Median

Example: Internists Salaries (x$1000)

127 132 138 141 144 146152154 165 171 177 192 241

Since n = 13 (odd,) then the median is themiddlemost or 7th measurement, Md=152

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Exercise

Page 96: Exercise SC 3-7

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Exercise SC 3-7

0.98 1.05 1.08 1.08 1.09 1.14 1.22 1.24 1.33 1.55

Median = 1.09 + 1.14 = 1.115

2

Mean = 11.76 = 1.176

10

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Page 94

m n 1 /2 F1

fmw Lm

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Median: Grouped Data

Interval Frequency0-49.99 78

50.00-99.99 123100.00-149.99 187150.00-199.99 82200.00-249.99 51250.00-299.99 47

300.00-349.99 13350.00-399.99 9400.00-449.99 6450.00-499.99 4

600

m

n 1 /2 F1 fm w Lm

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Page 96: Exercise SC 3-8

Interval Frequency100.00-149.5 12150.00-199.5 14200.00-249.5 27250.00-299.5 58

300.00-349.5 72350.00-399.5 63400.00-449.5 36450.00-499.5 18

m n 1 /2 F1

fmw Lm

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Page 97: Exercise 3-33

Interval Frequency0-24.9 5

25-49.9 1350-74.9 1675-99.9 8

100-124.9 6

m n 1 /2 F1

fmw Lm

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Page 97: Exercise 3-33

Interval Frequency Midpoint Product0-24.9 5

25-49.9 1350-74.9 1675-99.9 8

100-124.9 6

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Mode: Ungrouped Data

The mode, Moof a population or sample ofmeasurements is the measurement that

occurs most frequently.

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Page 103: Exercise SC 3-9

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Page 103: Exercise 3-38

Books checked out (x) 0 1 2 3 4 5 6 7

Frequency (f) 3 3 7 3 2 1 0 1

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Page 99

Mo LMO d1

d1 d

2

w

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Mode: Grouped Data

Interval Frequency0-49.99 78

50.00-99.99 123100.00-149.99 187150.00-199.99 82

200.00-249.99 51250.00-299.99 47300.00-349.99 13350.00-399.99 9400.00-449.99 6

450.00-499.99 4600

Mo LMO

d1

d1 d

2

w

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Page 103: Exercise SC 3-10

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Page 103: Exercise SC 3-10

Class Frequency15-19 1020-24 925-29 330-34 4

35 4

Mo LMO

d1

d1 d

2

w

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Measures of Central Tendency

Mean: Ungrouped Data

Grouped Data

Median: Ungrouped Data

Grouped Data

Mode: Ungrouped Data

Grouped Data