Practical Statistics
Descriptive Statistics
There are six statistics that will
answer 90% of all questions!
There six are:
1. Descriptive
There six are:
1. Descriptive
2. Chi-square
There six are:
1. Descriptive
2. Chi-square
3. Z-tests
There six are:
1.
2.
3.
4.
Descriptive
Chi-square
Z-tests
t-tests
There six are:
5. Correlation (association)
There six are:
5. Correlation
6. Regression
Descriptive Statistics
These are utilized to describe the characteristic
of a population (parameter), or
the 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
Geodemography
Geodemography
2012 Map
http://www.geocurrents.info/2012/11#!gallery/6/
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
5
Frequency
4
3
2
1
Mean =68.975
Std. Dev. =4.76896
N =40
0
60.00
65.00
70.00
VAR00001
75.00
On SPSS: Open the file called WeldDat.sav
Do the following:
Graphs
Graphboard Template…
Select WeldTime
Select histogram with Normal…
OK
Descriptive Statistics
Simple counts: histograms
5
Frequency
4
3
2
1
Mean =68.975
Std. Dev. =4.76896
N =40
0
60.00
65.00
70.00
VAR00001
75.00
Descriptive Statistics
Simple counts: ogive
100.0%
Cumulative Percent
80.0%
60.0%
40.0%
20.0%
0.0%
60.00
65.00
70.00
VAR00001
75.00
80.00
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 Statistics
Central tendency:
A single number to represent a group.
Statistics
Time
N
Mean
Std. Error of Mean
Median
Mode
Std. Deviation
Skewness
Std. Error of Skewness
Kurtos is
Std. Error of Kurtosis
Sum
Valid
Missing
40
0
68.9750
.75404
69.0000
73.00
4.76896
-.379
.374
-.985
.733
2759.00
Descriptive Statistics
The average is 68.98.
The standard deviation is 4.77.
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 Statistics
Central tendency:
1. Mode
The most frequent score.
Descriptive Statistics
Central tendency:
1. Mode
2. Median
Half the numbers are larger, half are smaller.
Descriptive Statistics
Central tendency:
1. Mode
2. Median
3. Mean
The center of gravity of a distribution
Descriptive Statistics
Central tendency:
1. Mode
2. Median
3. Mean
Arithmetic
Harmonic
Geometric
Descriptive Statistics
Central tendency:
1. Mode
2. Median
3. Mean
Arithmetic
n
x
x
i 1
n
i
Descriptive Statistics
Central tendency:
3. Mean
Harmonic
Clayson Power Data
180
160
140
120
100
80
60
40
20
0
1/6/00 1/2/02 1/10/03 1/6/05 1/2/07 1/10/08 1/6/10 1/2/12 1/10/13 1/6/15
Legend
Temp
KWH
Cost
Descriptive Statistics
Central tendency:
3. Mean
Harmonic
Clayson Power Data
80
70
60
50
40
30
20
10
0
1/6/00 1/2/02 1/10/03 1/6/05 1/2/07 1/10/08 1/6/10 1/2/12 1/10/13 1/6/15
Legend
Temp
Descriptive Statistics
Central tendency:
3. Mean
Harmonic
Clayson Power Data
80
70
60
Legend
Temp
Linear Trend
50
40
30
20
10
0
1/5/00 1/1/02 1/9/03 1/5/05 1/1/07 1/9/08 1/5/10 1/1/12 1/9/13 1/5/15
Descriptive Statistics
Central tendency:
1. Mode
2. Median
3. Mean
Harmonic
n
1 1
1
 
H n i 1 xi
Descriptive Statistics
Central tendency:
1. Mode
2. Median
3. Mean
Geometrical (For pure ratio numbers)
G
 x 
n
i 1 i
1
n
Geometric Mean:
Does pricing following perception or volume?
If a package holds twice as much should it be
priced as twice that of a
package that holds half
as much?
Problem: Customers do not perceive volume correctly.
Geometric Mean:
Does pricing following perception or volume?
The perception of volume follows:
Seven’s Law:
  kS
How should this be done?
p
Descriptive Statistics
Measure of Variation:
Again a single number to represent a group.
Statistics
Time
N
Std. Error of Mean
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtos is
Std. Error of Kurtosis
Range
Minimum
Maximum
Valid
Missing
40
0
.75404
4.76896
22.743
-.379
.374
-.985
.733
16.00
60.00
76.00
Descriptive Statistics
Measure of Variation:
1. Range
a. (Highest – Lowest) + 1
b. Subject to deviancy
Descriptive Statistics
Measure of Variation:
1. Range
2. Mean Deviation
a. Problem: Variation logically would be
the average deviation around a measure
of central tendency.
 x  x / n
i
Descriptive Statistics
Measure of Variation:
1. Range
2. Mean Deviation
a. Problem: But…
 x  x  0
i
Always!!
Descriptive Statistics
Measure of Variation:
1. Range
2. Mean Deviation
a. Problem: So negative can be removed by
looking at the absolute value.
Abs(  xi  x ) / n
Descriptive Statistics
Measure of Variation:
1. Range
2. Mean Deviation
a. Problem: Negative can be removed
by squaring the value.
 x
i
 x / n
2
Descriptive Statistics
Measure of Variation:
1. Range
2. Mean Deviation
a. Problem: This is the definition of:
3. Variance
 x
i
 x  / (n  1)
2
Descriptive Statistics
Measure of Variation:
1. Range
2. Mean Deviation
3. Variance
a. Problem: This is difficult to work with
descriptively, so the square root can be taken.
x  x
n
Sx 
i 1
i
n 1
2
Descriptive Statistics
Measure of Variation:
1. Range
2. Mean Deviation
3. Variance
a. This is called the:
4. Standard Deviation
x  x
n
Sx 
i 1
i
n 1
2
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 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. 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
Time
N
Mean
Std. Error of Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtos is
Std. Error of Kurtosis
Range
Minimum
Maximum
Valid
Missing
40
0
68.9750
.75404
69.0000
73.00
4.76896
22.743
-.379
.374
-.985
.733
16.00
60.00
76.00
a. Give the central tendency measures of this sample.
b. What is the range, variance and standard deviation?
Statistics
Time
N
Mean
Std. Error of Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtos is
Std. Error of Kurtosis
Range
Minimum
Maximum
Valid
Missing
40
0
68.9750
.75404
69.0000
73.00
4.76896
22.743
-.379
.374
-.985
.733
16.00
60.00
76.00
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
Time
N
Mean
Std. Error of Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtos is
Std. Error of Kurtosis
Range
Minimum
Maximum
Valid
Missing
40
0
68.9750
.75404
69.0000
73.00
4.76896
22.743
-.379
.374
-.985
.733
16.00
60.00
76.00
a.
b.
c.
d.
Give the central tendency measures of this sample.
What is the range, variance and standard deviation?
Explain what you now know about the time it takes to make welds.
When should a worker be reprimanded or fired for working
too slow?
Statistics
Time
N
Mean
Std. Error of Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtos is
Std. Error of Kurtosis
Range
Minimum
Maximum
Valid
Missing
40
0
68.9750
.75404
69.0000
73.00
4.76896
22.743
-.379
.374
-.985
.733
16.00
60.00
76.00