Exam 4: Understanding and Comparing Distributions

The weekly salaries (in dollars)of 24 randomly selected employees of a company are shown below. 310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700

Here is a histogram of the assets (in millions of dollars)of 71 companies. Which of the following is an appropriate re-expression of these data? (More than one may be appropriate.) I II III

The Ontario Ministry of Education collects data on the number of years of teaching experience of high school teachers.A sample taken this year of 19 high school teachers yielded the following data on number of years of teaching experience. 16 28 1 33 15 6 18 7 20 14 17 19 16 10 21 29 14 39 18

For which class are the mean and median most different?

The test scores of 15 students are listed below. 33 60 50 65 66 68 70 73 74 77 78 82 87 90 99

For class 2,compare the mean and the median.

Which class had the smallest IQR?

The centre for health in a certain country compiles data on the length of stay by patients in short-term hospitals and publishes its statistical findings annually.Data from a sample of 67 male patients and 63 female patients on length of stay (in days)are displayed in the histograms below. i)What would you suggest be changed about these histograms to make them easier to compare? ii)Describe these distributions by writing a few sentences comparing the duration of hospitalization for men and women. iii)Can you suggest a reason for the peak in women's length of stay?

How would you describe the shape of each distribution?

The weights (in kilograms)of 27 dogs are listed below. 1.2 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.7 2.8 2.8 2.8 2.9 2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2

Here are the test scores of 32 students: 35 37 41 44 46 48 53 55 56 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 80 82 83 86 89 92 95 99

Which class had the highest mean score?

The histograms show the cost of living,in dollars,for 32 Canadian cities.The histogram on the left shows the cost of living for the 32 cities using bins $10 wide,and the histogram on the right displays the same data using bins that are $6 wide. Compare the distributions (shape,centre,spread,unusual features).

Here are the summary statistics for mathematics scores for one high school graduating class,and the parallel boxplots comparing the scores of male and female students.Write a brief report on these results.Be sure to discuss shape,centre,and spread of the scores. Mean Median SD Min Max Q1 Q3 Male 17 60 63 18.6 30 100 52 78 Female 18 65 66 17.7 36 98 50 80

Here are boxplots of the points scored during the first 10 games of the basketball season for both Caroline and Alexandra.Summarize the similarities and differences in their performance so far.

Do men and women run a 5-kilometre race at the same pace? Here are boxplots of the time (in minutes)for a race recently run in Victoria,B.C.Write a brief report discussing what these data show.

Here is a histogram of the assets (in millions of dollars)of 71 companies.The logarithm re-expression of assets is also given.In the logarithm re-expression,what does the value 2.25 actually indicate about the company's assets?

The boxplots display case prices (in dollars)of white wines produced by three vineyards in south-western Ontario.Describe these wine prices.

Here is a histogram of the assets (in millions of dollars)of 71 companies. Which of the following is the most appropriate re-expression of these data? Explain. I II III

The boxplots display case prices (in dollars)of white wines produced by three vineyards in south-western Ontario.Which vineyard produces the most expensive wine?