1. 3-2Measures of Variation
Chapter(3)
3-2Measures of Variation
Instructor: Alaa saud
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2. Example 3-18:
A testing lab wishes to test two experimental brands of outdoor paint to see how long each will last before fading. The testing lab makes 6 gallons of each paint to test. Since different chemical agents are added to each group and only six cans are involved, these two groups constitute two small populations . The results (in months)are shown. Find the mean of each group.
Brand A
Brand B 10 35 60 45 50 30 40 20 25
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3. The mean for brand A is The mean for brand B is
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4. 1- Range
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5. Find the ranges for the paints in Example 3-18 .
The range for brand A is
The range for brand B is
R= 60 – 10 = 50 months
R= 45 – 25 = 20 months
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6. Example 3-20:
The salaries for the staff of the XYZ . Manufacturing Co are shown here. Find the range.
Staff
Salary
Owner
$100,000
Manger
40,000
Sales representative
30,000
workers
25,000
15,000
18,000
The range is R= $100,000- $ 15,000 = $85,000
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7. 2-Variance
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8. The variance is the average of the squares of
the distance each value is from the mean.
population
Sample
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9. 3-The standard deviation
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10. The standard deviation is the square root of the variance.
population
Sample

11. Example 3-21:
Find the variance and standard deviation for the data set for brand A paint in Example 3-18.
Brand A
Brand B 10 35 60 45 50 30 40 20 25
Solution :.
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12. Example 3-23:
Find the sample variance and standard deviation for the amount of European auto sales for a sample of 6 years shown .T he data are in million dollars.
11.2 , 11.9 , 12.0 , 12.8 , 13.4 , 14.3
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14. Coefficient of Variation
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15. coefficient of variation
The coefficient of variation , denoted by Cvar is the standard deviation divided by the mean . T he result is expressed as a percentage.
population
Sample
A statistic that allows you to compare standard deviations when the units are different , as in this example is called the
coefficient of variation
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16. Since the coefficients of variation is larger for commission.
Example 3-25:
The mean of the number of sales of cars over a 3-month period is 87 and the standard deviation is 5. The mean commission is $5225 and standard deviation is $773. Compare the variations of the two.
Since the coefficients of variation is larger for commission.
The commission are more variable than the sales.
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17. Example 3-25:
The mean for the number of pages of sample of women’s fitness magazines is 132 with a variance of 23.The mean for the number of advertisements of sample of women’s fitness magazines is 182 with a variance of 62. Compare the variations.
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19. For example : Then the data fall between 570 and 390
, approximately 68%
Then the data fall between 570 and 390
, approximately 95%
Then the data fall between 660 and 300
approximately 99.7%
Then the data fall between 750 and 210
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20. Exercises:
Q(1):When a distribution is bell-shaped, approximately what percentage of data values will fall within 1
standard deviation of the mean?
A) 99.7%
B) 95%
C) 50%
D) 68%
Q(2):Math exam scores have a bell-shaped distribution with a mean of 100 and standard deviation of 15 . use the empirical rule to find the percentage of students with scores between 70 and 130?
Q(3):A set of 49 data values has the variance 36, then the standard deviation is
A) B) C) D) 1.36
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