Practical Statistics Descriptive Statistics. There are six statistics that will answer 90% of all questions!

Practical Statistics

Descriptive Statistics

There are six statistics that will

answer 90% of all questions!

There six are:

1. Descriptive

There six are:

1. Descriptive2. Chi-square

There six are:

1. Descriptive2. Chi-square3. Z-tests

There six are:

1. Descriptive2. Chi-square3. Z-tests4. t-tests

There six are:

5. Correlation (association)

There six are:

5. Correlation6. Regression


These are utilized to describe the characteristicof a population (parameter), orthe characteristics of a sample (a statistic)

Many business problems can be solved by knowing only descriptive statistics.

Geodemography

http://www.youtube.com/watch?v=7UCxzYpXhpI

http://www.youtube.com/watch?v=7UCxzYpXhpI

Geodemography


Simple counts: frequency


Simple counts: frequency

The amount of time (in seconds) needed for assembly-line workers to complete a weld was recorded for 40 workers.

69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67

a. What is the frequency for each amount of time?


Simple counts: histograms

VAR0000175.0070.0065.0060.00

Fre

qu

en

cy

5

4

3

2

1

0

Mean =68.975Std. Dev. =4.76896

N =40


Simple counts: histograms

VAR0000175.0070.0065.0060.00

Fre

qu

en

cy

5

4

3

2

1

0

Mean =68.975Std. Dev. =4.76896

N =40


Simple counts: ogive

http://mathworld.wolfram.com/Ogive.html

http://mathworld.wolfram.com/Ogive.html

Symmetry

Right Left


Back to the workers making welds…..


69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67

Descriptive StatisticsCentral tendency: A single number to represent a group.

Statistics

Time40

0

68.9750

.75404

69.0000

73.00

4.76896

-.379

.374

-.985

.733

2759.00

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Skewness

Std. Error of Skewness

Kurtosis

Std. Error of Kurtosis

Sum


The standard deviation is 4.77. The average is 68.98.


69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67

Descriptive StatisticsCentral tendency: 1. Mode

The most frequent score.

Descriptive StatisticsCentral tendency: 1. Mode2. Median

Half the numbers are larger, half are smaller.

Descriptive StatisticsCentral tendency: 1. Mode2. Median3. Mean

The center of gravity of a distribution


ArithmeticHarmonicGeometric


Arithmetic

xx

n

ii

n

1

Descriptive StatisticsCentral tendency: 3. Mean

HarmonicClayson Power Data

1/6/00 1/2/02 1/10/03 1/6/05 1/2/07 1/10/08 1/6/10 1/2/120

20

40

60

80

100

120

140

160

180

LegendTempKWHCost

Descriptive StatisticsCentral tendency: 3. Mean

Harmonic Clayson Power Data

1/5/00 1/1/02 1/9/03 1/5/05 1/1/07 1/9/08 1/5/10 1/1/120

10

20

30

40

50

60

70

80

LegendTempLinear Trend


Harmonic

1 1 1

1H n x ii

n


Geometrical (For ratio numbers)

G xi

n

in 1

1

Geometric Mean:

Does pricing following perception or volume?If a package holds twice as much, should it bepriced as twice that of a package that holds half asmuch?

Problem: Customers do not perceive volume correctly.

Geometric Mean:

Does pricing following perception or volume?

The perception of volume follows:

Seven’s Law:

kS p

How should this be done?


Measure of Variation: Again a single number to represent a group.

Statistics

Time40

0

.75404

4.76896

22.743

-.379

.374

-.985

.733

16.00

60.00

76.00

Valid

Missing

N

Std. Error of Mean

Std. Deviation

Variance

Skewness


Kurtosis


Range

Minimum

Maximum

Population: mean = 10 SD = 5

Population: mean = 10 SD = 2.5

Population: mean = 10 SD = 1

Population: mean = 10 SD = 0.5


Measure of Variation: 1. Range

a. (Highest – Lowest) + 1b. Subject to deviancy


Measure of Variation: 1. Range2. Mean Deviation

a. Problem: Variation logically would be the average deviation around a measure

of central tendency.

x x ni /



a. Problem: But…

x xi 0Always!!



a. Problem: So negative can be removed by looking at the absolute value.

Abs x x ni( ) /



a. Problem: Negative can be removed by squaring the value.

x x ni 2/



a. Problem: This is the definition of: 3. Variance

x x ni 21/ ( )


Measure of Variation: 1. Range2. Mean Deviation3. Variance

a. Problem: This is difficult to work with descriptively, so the square root can be taken.

S

x x

nx

ii

n

1

2

1


Measure of Variation: 1. Range2. Mean Deviation3. Variance

a. This is called the: 4. Standard Deviation

Sx x

nx

ii

n

1

2

1

The standard deviation is:

Roughly the average difference scores are from the average.

Or:

It is roughly the average difference between two measures taken from the same population.

It is an intuitive measure.

The amount of time (in seconds) needed for assembly-line workers tocomplete a weld was recorded for 40 workers.

69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67

Back to our welding times…..

a. Give the central tendency measures of this sample.

b. What is the range, variance and standard deviation?

c. Explain what you now know about the time it takes to make welds.

d. When should a worker be reprimanded or fired for working too slow?

a. Give the central tendency measures of this sample.

Statistics

Time40

0

68.9750

.75404

69.0000

73.00

4.76896

22.743

-.379

.374

-.985

.733

16.00

60.00

76.00

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness


Kurtosis


Range

Minimum

Maximum

a. Give the central tendency measures of this sample.b. What is the range, variance and standard deviation?

Statistics

Time40

0

68.9750

.75404

69.0000

73.00

4.76896

22.743

-.379

.374

-.985

.733

16.00

60.00

76.00

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness


Kurtosis


Range

Minimum

Maximum

a. Give the central tendency measures of this sample.b. What is the range, variance and standard deviation?c. Explain what you now know about the time it takes to make welds.

Statistics

Time40

0

68.9750

.75404

69.0000

73.00

4.76896

22.743

-.379

.374

-.985

.733

16.00

60.00

76.00

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness


Kurtosis


Range

Minimum

Maximum

a. Give the central tendency measures of this sample.b. What is the range, variance and standard deviation?c. Explain what you now know about the time it takes to make welds.d. When should a worker be reprimanded or fired for working too slow?

Statistics

Time40

0

68.9750

.75404

69.0000

73.00

4.76896

22.743

-.379

.374

-.985

.733

16.00

60.00

76.00

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness


Kurtosis


Range

Minimum

Maximum

Service Encounter and Personality

How many respondents do we have, andwhat is their sex?


What is their average age?


How satisfied were they with their service encounter?


How satisfied were they with their service encounter?

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Practical Statistics Descriptive Statistics. There are six statistics that will answer 90% of all questions!