practical statistics descriptive statistics. there are six statistics that will answer 90% of all...
TRANSCRIPT
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
Descriptive Statistics
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
Descriptive Statistics
Simple counts: frequency
Descriptive Statistics
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?
Descriptive Statistics
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
Descriptive Statistics
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
Descriptive Statistics
Simple counts: ogive
http://mathworld.wolfram.com/Ogive.html
Symmetry
Right Left
Descriptive Statistics
Back to the workers making welds…..
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
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
Descriptive Statistics
The standard deviation is 4.77. The average is 68.98.
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
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
Descriptive StatisticsCentral tendency: 1. Mode2. Median3. Mean
ArithmeticHarmonicGeometric
Descriptive StatisticsCentral tendency: 1. Mode2. Median3. Mean
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
Descriptive StatisticsCentral tendency: 1. Mode2. Median3. Mean
Harmonic
1 1 1
1H n x ii
n
Descriptive StatisticsCentral tendency: 1. Mode2. Median3. Mean
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?
Descriptive Statistics
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
Std. Error of Skewness
Kurtosis
Std. Error of 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
Descriptive Statistics
Measure of Variation: 1. Range
a. (Highest – Lowest) + 1b. Subject to deviancy
Descriptive Statistics
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 /
Descriptive Statistics
Measure of Variation: 1. Range2. Mean Deviation
a. Problem: But…
x xi 0Always!!
Descriptive Statistics
Measure of Variation: 1. Range2. Mean Deviation
a. Problem: So negative can be removed by looking at the absolute value.
Abs x x ni( ) /
Descriptive Statistics
Measure of Variation: 1. Range2. Mean Deviation
a. Problem: Negative can be removed by squaring the value.
x x ni 2/
Descriptive Statistics
Measure of Variation: 1. Range2. Mean Deviation
a. Problem: This is the definition of: 3. Variance
x x ni 21/ ( )
Descriptive Statistics
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
Descriptive Statistics
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
Std. Error of Skewness
Kurtosis
Std. Error of 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
Std. Error of Skewness
Kurtosis
Std. Error of 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
Std. Error of Skewness
Kurtosis
Std. Error of 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
Std. Error of Skewness
Kurtosis
Std. Error of Kurtosis
Range
Minimum
Maximum
Service Encounter and Personality
How many respondents do we have, andwhat is their sex?
Service Encounter and Personality
What is their average age?
Service Encounter and Personality
How satisfied were they with their service encounter?
Service Encounter and Personality
How satisfied were they with their service encounter?