BarnumVictoriaLabManual Section 2.1

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Section 2.1 1. BOSTON COMMUTE TIME The accompanying table summarizes daily commute times in Boston. How many commute times are included in the summary? Is it possible to identify the exact values of all of the original data amounts? 1000 commute times are included in the summary, no it is not possible to the exact values, these are estimates provided by the participants. 2. BOSTON COMMUTE TIME Refer to the accompanying frequency distribution. What problem would be created by using classes of 0–30, 30–60, . . . , 120–150? The widths are not the same, lower limits are being used to calculate the class width. To calculate correctly it would need to be 0-29, 30-59,ect 3. RELATIVE FREQUENCY DISTRIBUTION Use percentages to construct the relative frequency distribution corresponding to the accompanying frequency distribution for daily commute time in Boston. Percentage for aclass = frequency for a class ∑ of allfrequencies ∗ 100 0-29: 468 1000 ∗ 100 = 46.8% 30-59: 422 1000 *100 = 42.2 % 60-89: 92 1000 ∗ 100 = 9.2% 90-119: 10 1000 *100 = 1.0 % 120-149: 8 1000 ∗ 100 = 0.8 %

4. WHAT’S WRONG? Heights of adult males are known to have a normal distribution, as described in this section. A researcher claims to have randomly selected adult males and measured their heights with the resulting relative frequency distribution as shown in the margin. Identify two major flaws with these results. The results from the participants do not show the typical patterns of normal distribution, the lowest height and highest height range, 130 – 144 and 190 – 204 are showing frequencies that are increased while the middle height range, 160-174 shows a decrease. Typically, the lowest range would reflect an increase until there is a peak within the range in the middle of the classes. Then there would be a subtle decrease with the higher ranges of class. The second flaw would be that the data is not symmetric. The data does not look like a mirror image of each other but looks like it changes frequently from increase to decrease and has not identifiable or correlation to pattern. It looks like randomized data. In Exercises 5–8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B. 5.

formula for class width: ( maximumdata value ) −( minimumdata value ) number of classes formula for class midpoint : ( lower classlimit ) +( upper classlimit ) 2 Class width: 80 − 21 7 ≈ 10 Class midpoint: 20 + 29 2 = 24.5, 30 + 39 2 =34.5, 40 + 49 2 =44.5, 50 + 59 2 =54.5, 60 + 69 2 = 64.5, 70 + 79 2 =74.5, 80 + 89 2 =84.5

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Class Boundaries: 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5 Number of individuals: 31+34+15+3+6+1+1 = 91 individuals Class width: 76 − 29 6 ≈10 Class midpoint: 20 + 29 2 = 24.5, 30 + 39 2 =34.5, 40 + 49 2 =44.5, 50 + 59 2 =54.5, 60 + 69 2 = 64.5, 70 + 79 2 =74.5 Class Boundaries: 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 Number of individuals: 1+29+38+16+6+1 = 91 individuals

Class Width: 646 − 75 6 ≈100 Class Midpoint: 0 + 99 2 = 49.5, 100 + 199 2 =149.5, 200 + 299 2 =249.5, 300 + 399 2 =349.5, 400 + 499 2 = 449.5, 500 + 599 2 =549.5, 600 + 699 2 =649.5 Class Boundaries : -0.5, 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5 Number of individuals: 1+51+90+10+0+0+1 = 153 individuals

Class Width: 575 − 132 5 ≈100 Class Midpoint : 100 + 199 2 =149.5, 200 + 299 2 =249.5, 300 + 399 2 =349.5, 400 + 499 2 = 449.5, 500 + 599 2 =549.5 Class Boundaries : 99.5, 199.5, 299.5, 399.5, 499.5, 599.5 Number of individuals: 25+92+28+0+2 = 147 individuals 9. BEST ACTRESSES: No, it is not a normal distribution, due the increase on the second class and middle classes, it does not have the typical mirrored data. Without the lower and highest classes data being mirrored, the data cannot be normal distribution .

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10. BEST ACTORS: No, it is not a normal distribution , the data cannot be mirrored for the two lowest and highest classes due to the swift increase for the class for the age groups 30-39 and 40- 49; and then sudden decrease within the older of age classes . In addition, the peak for the highest frequency would ideally be within the classes of 40-49 & 50-59. Instead, the peak frequency is at the ages of 40-49 and there is a swift decrease within the age group of 50-59 class and continues until the class for the age group 70-79 class.

11. BLOOD PLATELET COUNTS OF MALES: Yes, it would be a normal distribution for the frequency distribution. With the data creating a bell shape with the peaks of frequency being 100-199 and 200-299 and the data being mirrored for the both the lower classes of platelets and highest platelets, excluding the platelets for 600-699 create a bell shape.

12. BLOOD PLATELET COUNTS OF FEMALES: Yes, it would not be a normal distribution, the frequencies started low, then had a peak at 100-199 then proceed to decrease. The data then created a belled like and symmetric shape.

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13. No, the data appears to be not normal distribution. The frequency peaks, at the class 15-29 with the total frequency being 16 and has a steady decline with the frequency. This would prevent the frequencies from mirroring each other.

14. Yes, this data would be a normal distribution, with the frequency peaking with the ages of 50-54 and 55-59 and the symmetric shape of the lower and higher class limits, a bell shape appears and the frequencies somewhat mirror each other. 15.

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