INFO HW
danya.alsinan
2INFO1010SingleVariableDescriptiveStats.pptxINFO 1010
CHARTS AND DESCRIPTIVE STATISTICS
‹#›
1
Joe’s Diner Example
Guests eating at Joe’s Diner were asked to rate the
quality of their meal as being excellent,
above average, average, below average, or poor. The
ratings provided by a sample of 20 customers are:
Below Average
Above Average
Above Average
Average
Above Average
Average
Above Average
Average
Above Average
Below Average
Poor
Excellent
Above Average
Average
Above Average
Above Average
Below Average
Poor
Above Average
Average
Frequency Distribution
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Frequency Distribution
Poor
Below Average
Average
Above Average
Excellent
2
3
5
9
1
Total 20
Rating
Frequency
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Using Excel’s COUNTIF Function to Construct a Frequency Distribution
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Using Excel’s COUNTIF Function to Construct a Frequency Distribution
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Relative Frequency and Percent Frequency Distributions
Poor
Below Average
Average
Above Average
Excellent
.10
.15
.25
.45
.05
Total 1.00
10
15
25
45
5
100
Relative
Frequency
Percent
Frequency
Rating
.10(100) = 10
1/20 = .05
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Using Excel to Construct Relative Frequency and Percent Frequency Distributions
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Using Excel to Construct Relative Frequency and Percent Frequency Distributions
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Poor
Below
Average
Average
Above
Average
Excellent
Frequency
Rating
Bar Chart
1
2
3
4
5
6
7
8
9
10
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Histogram
Another common graphical display of quantitative data is a histogram.
The variable of interest is placed on the horizontal axis.
A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency, relative frequency, or percent frequency.
Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes.
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Histogram Days on Market for Home Sales
2
4
6
8
10
12
14
16
18
Frequency
10-19 20-29 30-39 40-49 50-59 60-69
When the Format Data Series dialog box appears Set the Gap Width to 0
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Symmetric
Histograms Showing Skewness
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Left tail is the mirror image of the right tail
Examples: Heights of People
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Histograms Showing Skewness
Moderately Skewed Left
A longer tail to the left
Example: Exam Scores
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
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Moderately Right Skewed
Histograms Showing Skewness
A Longer tail to the right
Example: Housing Values
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
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Histograms Showing Skewness
Highly Skewed Right
A very long tail to the right
Example: Executive Salaries
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
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Distribution Shape: Skewness
An important measure of the shape of a distribution is called skewness.
The formula for the skewness of sample data is
Skewness =
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Distribution Shape: Skewness
Symmetric (not skewed)
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Skewness = 0
Skewness is zero.
Mean and median are equal.
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Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Distribution Shape: Skewness
Moderately Skewed Left
Skewness = - .31
Skewness is negative.
Mean will usually be less than the median.
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Distribution Shape: Skewness
Moderately Skewed Right
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Skewness = .31
Skewness is positive.
Mean will usually be more than the median.
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Distribution Shape: Skewness
Highly Skewed Right
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Skewness = 1.25
Skewness is positive (often above 1.0).
Mean will usually be more than the median.
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Seventy efficiency apartments were randomly
sampled in a college town. The monthly rent prices
for the apartments are listed below in ascending order.
Distribution Shape: Skewness
Example: Apartment Rents
525
530
530
535
535
535
535
535
540
540
540
540
540
545
545
545
545
545
550
550
550
550
550
550
550
560
560
560
565
565
565
570
570
572
575
575
575
580
580
580
580
585
590
590
590
600
600
600
600
610
610
615
625
625
625
635
649
650
670
670
675
675
680
690
700
700
700
700
715
715
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Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Skewness = .92
Distribution Shape: Skewness
Example: Apartment Rents
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A
B
C
D
1
Quality Rating
Quality Rating
Frequency
2
Above Average
Poor
=COUNTIF($A$2:$A$21,C2)
3
Below Average
Below Average
=COUNTIF($A$2:$A$21,C3)
4
Above Average
Average
=COUNTIF($A$2:$A$21,C4)
5
Average
Above Average
=COUNTIF($A$2:$A$21,C5)
6
Average
Excellent
=COUNTIF($A$2:$A$21,C6)
7
Above Average
Total
=SUM(D2:D6)
8
Above Average
A
B
C
D
1
Quality Rating
Quality Rating
Frequency
2
Above Average
Poor
2
3
Below Average
Below Average
3
4
Above Average
Average
5
5
Average
Above Average
9
6
Average
Excellent
1
7
Above Average
Total
20
8
Above Average
C
D
E
F
1
Quality Rating
Frequency
Relative
Frequency
Percent
Frequency
2
Poor
=COUNTIF($A$2:$A$21,C2)
=D2/$D$7
=E2*100
3
Below Average
=COUNTIF($A$2:$A$21,C3)
=D3/$D$7
=E3*100
4
Average
=COUNTIF($A$2:$A$21,C4)
=D4/$D$7
=E4*100
5
Above Average
=COUNTIF($A$2:$A$21,C5)
=D5/$D$7
=E5*100
6
Excellent
=COUNTIF($A$2:$A$21,C6)
=D6/$D$7
=E6*100
7
Total
=SUM(D2:D6)
=SUM(E2:E6)
=SUM(F2:F6)
8
C
D
E
F
1
Quality Rating
Frequency
Relative
Frequency
Percent
Frequency
2
Poor
2
0.10
10
3
Below Average
3
0.15
15
4
Average
5
0.25
25
5
Above Average
9
0.45
45
6
Excellent
1
0.05
5
7
Total
20
1.00
100
8
