Download 155S3.3.notebook 1 January 22, 2010

155S3.3.notebook
January 22, 2010
MAT 155­DY1 & DY 2
Section 3.3 Measures of Variation
Jan 20­7:16 AM
Section 3­3 Measures of Variation By formula find range, variance, and standard deviation.
115.8. Listed below are intervals (in minutes) between eruptions of the Old Faithful geyser in Yellowstone National Park. Based on the results, is an interval of 100 minutes unusual?
98 92 95 87 96 90 65 92 95 93 98 94
Jan 20­7:16 AM
Section 3­3 Measures of Variation Use TI to find range, variance, and standard deviation.
116/16. Researchers at Pennsylvania State University conducted experiments with poplar trees. Listed below are weights (kg) of poplar trees given no treatment and poplar trees treated with fertilizer and irrigation. Does there appear to be a difference between the two standard deviations?
No treatment:
0.15 0.02 0.16 0.37 0.22
Treatment: 2.03 0.27 0.92 1.07 2.38
No Treatment has smaller standard deviation meaning that weights are closer together than those in the Treatment group. However, the Treatment group has a much larger mean.
Jan 20­7:16 AM
Jan 20­9:05 AM
Section 3­3 Measures of Variation By formula find range, variance, and standard deviation.
115.10. Listed below are body temperatures from eight adults collected by researchers at the University of Maryland. Based on the results, is a body temperature of 104.0oF unusual? Why or why not? What should be done with someone having a body temperature of 104.0oF?
98.6 98.6 98.0 98.0 99.0 98.4 98.4 98.4
Jan 20­7:16 AM
Section 3­3 Measures of Variation Use TI to find range, variance, and standard deviation.
117/20. Listed below are BMI values from randomly selected men and women. Does there appear to be a difference in variation between the two data sets?
Men: 23.8 23.2 24.6 26.2 23.5 24.5 21.5 31.4 26.4 22.7 27.8 28.1
Women: 19.6 23.8 19.6 29.1 25.2 21.4 22.0 27.5 33.5 20.6 29.9 17.7
According to the means, women have a smaller BMI on the average. However, according to the standards of 2.79 and 4.91, women have more variation in BMI than men.
Jan 20­7:16 AM
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155S3.3.notebook
January 22, 2010
Section 3­3 Measures of Variation ­ Use Range Rule of Thumb.
Section 3­3 Measures of Variation ­ Use Range Rule of Thumb.
118/27. The given frequency distribution describes the speeds of drivers ticketed by the Town of Poughkeepsie police. These drivers were traveling through a 30 mph speed zone.
118/28. From Data Set 2, the accompanying frequency distribution summarizes a sample of human body temperatures. Find the standard deviation using the formula below. How does this compare with the standard deviation of 0.62 calculated from the original data using Formula 3­4?
L2 = f
L2= f
L1 = x
L3 = X2
L4 = f x
Section 3­3 Measures of Variation ­ Use Range Rule of Thumb.
118/30. From Data Set 1, the sample of 40 women have upper leg lengths with a mean of 38.86 cm and a standard deviation of 3.78 cm. Use range the rule of thumb to identify the minimum and maximum “usual” upper leg lengths. Is a length of 47.0 cm considered unusual in the context?
The minimum usual upper leg length is 31.30 cm.
The maximum usual upper leg length is 46.42 cm.
Jan 20­7:16 AM
Section 3­3 Measures of Variation ­ Use Empirical Rule
118/33. Heights of men have a bell­shaped distribution with a mean of 176 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of men between (b) 155 cm and 197 cm?
(a) 169 cm and 183 cm?
(b) 155 and 197 are three standard deviations to the left and right of the mean, respectively. Thus, about 99.7% of men would have a height between 155 cm and 197 cm.
Jan 20­7:16 AM
L3 = X2
L4 = f x
L5 = f X2
L5 = f X
Jan 20­7:16 AM
(a) 169 and 183 are one standard deviation to the left and right of the mean, respectively. Thus, about 68% of men would have a height between 169 cm and 183 cm.
L1 = x
2
Jan 20­7:16 AM
Section 3­3 Measures of Variation ­ Use Range Rule of Thumb.
118/32. From Data Set 15, aluminum cans with a thickness of 0.0111 in. have axial loads with a mean of 281.8 lb and standard deviation of 27.8 lb. Use the range rule of thumb to find the minimum and maximum “usual” axial loads. One particular can had an axial load of 504 lb. Is that unusual?
The minimum usual upper axial load is 226.2 lb.
The maximum usual upper axial load is 337.4 lb.
Jan 20­7:16 AM
Section 3­3 Measures of Variation ­ Use Empirical Rule
118/33. Heights of men have a bell­shaped distribution with a mean of 176 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of men between (b) 155 cm and 197 cm?
(a) 169 cm and 183 cm?
(a) 169 and 183 are one standard deviation to the left and right of the mean, respectively. Thus, about 68% of men would have a height between 169 cm and 183 cm.
(b) 155 and 197 are three standard deviations to the left and right of the mean, respectively. Thus, about 99.7% of men would have a height between 155 cm and 197 cm.
Jan 20­7:16 AM
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155S3.3.notebook
Section 3­3 Measures of Variation ­ use Coefficient of Variation
119/35. Use the sample data listed below to find the coefficient of variation for each of the two samples, then compare the results.
Heights (in.) of men:
71 66 72 69 68 69
Lengths (mm) of cuckoo eggs: 19.7 21.7 21.9 22.1 22.1 22.3 22.7 22.9 23.9
Heights: x­bar = 69.2 and s = 2.1 Thus, CV = 2.1/69.2 = 30.3%
Lengths: x­bar = 22.14 and s = 1.13 So, CV = 1.13/22.14 = 5.1%
There is more variation in the heights because CV = 30.3% is greater than CV = 5.1%. CAUTION! Do not make the mistake of thinking because s = 2.1 is greater than s = 1.13 means the CV for heights will be greater than CV for lengths. For example, if the mean for lengths were 3.1, we would get CV = 1.13/3.1 = 36.5% which is larger than 30.3%.
Jan 20­7:16 AM
January 22, 2010
Section 3­3 Measures of Variation ­ use Coefficient of Variation
119/35. Use the sample data listed below to find the coefficient of variation for each of the two samples, then compare the results.
Heights (in.) of men:
71 66 72 69 68 69
Lengths (mm) of cuckoo eggs: 19.7 21.7 21.9 22.1 22.1 22.3 22.7 22.9 23.9
Heights: x­bar = 69.2 and s = 2.1 Thus, CV = 2.1/69.2 = 3.03%
Lengths: x­bar = 22.14 and s = 1.13 So, CV = 1.13/22.14 = 5.1%
There is more variation in the heights because CV = 3.03% is greater than CV = 5.1%. CAUTION! Do not make the mistake of thinking because s = 2.1 is greater than s = 1.13 means the CV for heights will be greater than CV for lengths. For example, if the mean for lengths were 3.1, we would get CV = 1.13/3.1 = 36.5% which is larger than 30.3%.
Jan 20­7:16 AM
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