qba 260 business statistics
DESCRIPTION
QBA 260 Business Statistics. Chapter 5. Deviating from the Average. Compare two datasets (reported in inches) Dataset 1: 48, 46, 46, 49, 49, 47, 47, 46, 49 Dataset 2: 47, 51, 49, 53, 47, 45, 37, 38, 60 What is the average of each dataset? How are they different?. Comparing Datasets. Mean. - PowerPoint PPT PresentationTRANSCRIPT
QBA 260Business Statistics
Chapter 5
Deviating from the Average Compare two datasets (reported in
inches) Dataset 1: 48, 46, 46, 49, 49, 47, 47,
46, 49 Dataset 2: 47, 51, 49, 53, 47, 45, 37,
38, 60 What is the average of each
dataset? How are they different?
Comparing Datasets
Histogram - Dataset 1
0
2
4
6
8
10
10 20 30 40 50 60
Bin Categories
Num
ber w
ithin
each
bin
Histogram - dataset 2
0
2
4
6
8
10
10 20 30 40 50 60
Bin Categories
Num
ber w
ithin
eac
h bi
n
Mean (Average) for both datasets is 47.4 inchesVariances differ: Dataset 1 = 1.78 sq. inches, Dataset 2 = 51.03 sq. inches
Mean Mean
Variance and Deviations Variance is a measure of how much the
data points in a sample deviate from the sample mean
For data: x1, x2, x3,…, xn A deviation is the difference between a data
value and a central value such as the average
XXDeviation i
Deviations Dataset 1: 48,
46, 46, 49, 49, 47, 47, 46, 49
Average = 47.4 Deviations The average
deviation is (always) zero
Xi X-Bar Deviation
48 47.4 0.56
46 47.4 -1.44
46 47.4 -1.44
49 47.4 1.56
49 47.4 1.56
47 47.4 -0.44
47 47.4 -0.44
46 47.4 -1.44
49 47.4 1.56
47.4 0.00
(Average) (Sum)
Deviations Dataset 2: 47,
51, 49, 53, 47, 45, 37, 38, 60
Average = 47.4 Deviations The average
deviation is (always) zero
Xi X-Bar Deviation
47 47.4 -0.44
51 47.4 3.56
49 47.4 1.56
53 47.4 5.56
47 47.4 -0.44
45 47.4 -2.44
37 47.4 -10.44
38 47.4 -9.44
60 47.4 12.56
47.4 0.00
(Average) (Sum)
Populations and Samples Population
variance
Sample variance
N
XXN
1i
2i
2
)(
1N
XXs
N
1i
2i
2
)(
Sample Variance – Dataset 1 Sample variance
1
)(1
2
2
N
XXs
N
ii
1
22.142
N
s
78.119
22.142
s
Xi X-Bar Deviation Sq Dev
48 47.4 0.56 0.31
46 47.4 -1.44 2.09
46 47.4 -1.44 2.09
49 47.4 1.56 2.42
49 47.4 1.56 2.42
47 47.4 -0.44 0.20
47 47.4 -0.44 0.20
46 47.4 -1.44 2.09
49 47.4 1.56 2.42
47.4 0.00 14.22
(Average) (Sum) (Sum)
Sq Inches
Sample Variance – Dataset 2 Sample variance
1
)(1
2
2
N
XXs
N
ii
Xi X-Bar Deviation Sq Dev
47 47.4 -0.44 0.20
51 47.4 3.56 12.64
49 47.4 1.56 2.42
53 47.4 5.56 30.86
47 47.4 -0.44 0.20
45 47.4 -2.44 5.98
37 47.4 -10.44 109.09
38 47.4 -9.44 89.20
60 47.4 12.56 157.64
47.4 0.00 408.22
(Average) (Sum) (Sum)
1
22.4082
N
s
03.5119
22.4082
s Sq Inches
Variance and Standard Deviation The calculated variance is in a different
unit of measure than the original dataset Original Dataset measured in inches Variance measured in inches squared (due to
the use of squared deviations before we average them)
To accommodate this, we calculate the standard deviation which is the square root of the Variance
Standard Deviation Square root of the variance
1N
XXs
N
XX
N
1i
2i
N
1i
2i
)(
)(
Excel Functions
VARP(…) Population Variance VARPA(…) Population Variance
(includes cells that contain true/false data)
VAR(…) Sample Variance VARA(…) Sample Variance (includes
cells that contain true/false data)
Excel Functions STDEVP(…) Population Standard
Deviation STDEVPA(…) Population Standard
Deviation (includes cells that contain true/false data)
STDEV(…) Sample Standard Deviation STDEVA(…) Sample Standard Deviation
(includes cells that contain true/false data)
Average Absolute Deviation
Xi X-Bar Deviation ABS
48 47.4 0.56 0.56
46 47.4 -1.44 1.44
46 47.4 -1.44 1.44
49 47.4 1.56 1.56
49 47.4 1.56 1.56
47 47.4 -0.44 0.44
47 47.4 -0.44 0.44
46 47.4 -1.44 1.44
49 47.4 1.56 1.56
47.4 0.00 10.44
(Average) (Sum) (Sum)
Absolute Deviation = 10.44/9 = 1.16 EXCEL: AVEDEV