Assignment on Statistics.
We expect you to answer all questions using Excel and Upload the assignment as an .xls or .xlsx file through the Assignment folder on Blackboard. Please use a new tab for each question.
Since there are 12 questions, you will have 12 tabs with the answers.
You must show all intermediate steps of your work to receive full credit. You can earn a total of 70 points for this assignment
1. (6 points) Solid waste disposal has become a major problem for most cities. It is usually
fourth in cost behind education, police, and fire protection. On a statewide basis, the largest producers of solid municipal waste in 1997, in millions of tons per year, were
California 56.0
Texas 33.9 New York 30.2
Florida 23.8 Michigan 19.5
Illinois 13.3 North Carolina 12.6
The total amount of garbage created in all 50 states was 217 million tons.
(a) Create a Bar chart. (b) What proportion of the total solid waste is created in California? What proportion by the top
three states? What proportion by the top five states? (c) Does this mean that a person in California, Texas, or New York creates more garbage than
someone in another state? How would you adjust the figures to make that kind of comparison?
2. (6 points) In a study of the job hazards in the roofing industry in California, records of the
disabling injuries were classified according to the accident types. Of the total number of 1132 injuries, 329 were due to falls, 256 from burns, 219 from overexertion, 202 from being struck, 40
from foreign substance in eye, and 86 from other miscellaneous reasons. (Source: U.S. Dept. of HEW Publication NIOSH 75-176.) Present these data in a frequency table and
also give the relative frequencies.
3. (6 points) Of the $207 million raised by a major university's fund drive, $117 million came
from individuals and bequests, $24 million from industry and business, and $66 million from foundations and associations. Present this information in the form. of a pie chart.
4. (3 point) Data from one campus dorm on the number of complaints about the dorm food are collected each week of the semester. These weekly counts are to be grouped into classes 0-1, 2-3,
4-5, 7 or more. Both endpoints are included. Explain where a difficulty might arise.
5. (6 points) A sample of 50 departing airline passengers at the main check-in counter submitted the following number of bags to be checked through to final destinations.
0 1 2 2 1 2 1 2 3 0 1 0 1 1 0 1 3 0 1 2 1 1 1 2 1 2 2 1 2 0 0 2 2 1 1 1 1 1 1 1 2 0 1 3 0 1 2 1 1 3
(a) Create a bar chart with relative frequencies.
(b) Comment on the pattern. (c) What proportion of passengers who check in at the main counter fail to check any bags?
6. (6 points) Tornadoes kill many people every year in the United States. The number of lives annually lost over 54 years, from 1950 through 2003, is summarized in the following table.
Number of Deaths Frequency 24 or less 2
25-49 17 50-74 17
75-99 6 100-149 5
150-199 2 200-249 1
250 or more 3 Total 53
(a) Calculate the relative frequency for the intervals [0, 25), [25, 50) and so on where the
righthand endpoint is excluded. Take the last interval to be [250,550). (b) Plot the relative frequency histogram.(Hint: Since the intervals have unequal widths, make
the height of each rectangle equal to the relative frequency divided by the width of the interval. (c) What proportion of the years had 49 or fewer deaths due to tornadoes?
(d) Comment on the shape of the distribution.
7. (3 point) The height that bread rises may be one indicator of how light it will be. As a first
step, before modifying her existing recipe, a student cook measured the height (cm) the bread rises on eight occasions:
6.3 6.9 5.7 5.4 5.6 5.5 6.6 6.5. Find the mean and median of the raised heights.
8. (6 points) The following table gives the number of days in which selected metropolitan areas failed to meet air-quality standards in 1986, 1996, 2006 and 2016. We use the number of days
unhealthy plus the number of days very unhealthy as collected from https://www.epa.gov/outdoor-air-quality-data/air-quality-index-report
1986 1996 2006 2016
Atlanta 36 30 29 4 Baltimore 43 25 15 5
Boston 15 8 3 0 Chicago 42 11 4 5
Dallas 44 26 28 1 Detroit 18 19 3 0
Houston 66 35 31 1 Los Angeles 195 79 52 25
Miami 6 1 2 1 New York 56 31 21 2
Philadelphia 41 40 19 2 Phoenix
Pittsburgh 71 39 19 1
Washington, DC 40 19 21 0
(a) Find the data for Phoenix. (b) Find the sample mean and median for 1986, 1996, 2006 and 2016.
(c) What can you conclude from the difference between the mean and median about the distribution of air quality of metropolitan areas.
9. (6 points) A zoologist collected wild lizards in the Southwestern United States. Thirty lizards from the genus Phrynosoma were placed on a treadmill and their speed measured. The recorded
speed (meters/second) is the fastest time to run a half meter.
1.28 1.36 1.24 2.47 1.94 2.52 2.67 1.29 1.56 2.66 2.17 1.57 2.10 2.54 1.63 2.11
2.57 1.72 0.76 1.02 1.78 0.50 1.49 1.57 1.04 1.92 1.55 1.78 1.70 1.20
(a) Find the sample median, first quartile, and third quartile.
(b) Find the sample 90th percentile (c) Calculate null̅and s.
(d) Find the proportion of the observations that are in the intervals null̅ ± s, null̅ ± 2s, and null̅ ± 3s.
10. (6 points) For the dataset 8 6 14 4:
(a) Calculate the deviations (x - null̅) and check to see that they add up to 0. (b) Calculate the variance and the standard deviation.
11. (6 points) The city of Madison regularly checks the water quality at swimming beaches located on area lakes. In fifteen measurements, the concentration of fecal coliforms, in number of
Colony Forming Units (CFU) per 100 ml of water, was found during the summer at one beach.
180 1600 90 140 50 260 400 90 380 110 10 60 20 340 80
(a) Calculate the sample variance. (b) Calculate the sample standard deviation.
(c) One day, the water quality was bad-the reading was 1600 CFU-and the beach was closed. Drop this value and calculate the sample standard deviation for the days where the water quality
was suitable for swimming. Comment on the change.
12. (10 points) Replicate Figures 2.9 and 2.10 in Excel using the data from the website
mentioned in the Lecture notes.