BarnumVictoriaLabManual Section 2

.docx

School

Syracuse University *

*We aren’t endorsed by this school

Course

121

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by barnumv

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

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

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version