Exam 4: Understanding and Comparing Distributions

Here are some summary statistics for all of the runners in a local 12 kilometre race: Slowest time = 124 minutes Mean = 85 minutes Median = 85 minutes Range = 94 minutes IQR = 56 Q1 = 34 Standard deviation = 13 minutes Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

The mathematics department at a community college collected data for the number of students enrolled in 40 math courses over the course of one year.The following stem-and-leaf display shows the total number of students enrolled in each class. Key: 10 | 5 = 105 students

The weekly salaries (in dollars)of 24 randomly selected employees of a company are shown below,and displayed on the following boxplot. Find the mean and the median.Which is the most appropriate measure of centre?

Shown below are the boxplot and the histogram for the highest temperatures ever recorded (in °F)in 32 different states in the U.S.A. i)What features of the distribution can you see in both the histogram and the boxplot? ii)What features of the distribution can you see in the histogram that you could not see in the boxplot?

For class 2,compare the mean and the median.

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?

The following data consists of the heights,in centimetres,of 15 randomly selected female high school students and 15 randomly selected male high school students. Women: Men: Choose the back-to-back stemplot that represents the given data. I II III IV V

Which class had the smallest standard deviation?

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

Members of the Ontario Field Ornithologists (OFO)observe birds at various locations within the province to see how many different species of bird they can spot.Suppose that 21 members have reported spotting the following number of species in 2009.The lower stem contains leaves with the digits 0-4 and the upper stem contains leaves with digits 5-9. Key: 11 | 5 = 115 birds

Which class had the smallest IQR?

The freethrow percentages for participants in a basketball tournament were compiled.The percents ranged from 31% to 91% with a mean of 63% and a standard deviation of 6%.The quartiles and median percentages were 41%,79%,and 63%.Suppose one participant did not make any of his attempted freethrows (0%).Which of the summary statistics might not change if that data value was added to the distribution?

The histograms display the body fat percentages of 42 female students and 48 male students taking a college health course. Compare the distributions (shape,centre,spread,unusual features).

A small company employs a supervisor at $1,300 a week,an inventory manager at $900 a week,5 stock boys at $400 a week,and 3 drivers at $500 a week.

Which class had the largest standard deviation?

Which class do you think performed better on the test?

Here is an ogive of the distribution of students' marks on their statistics test. Choose the boxplot that represents the given data. I II III IV V

Here is a histogram of the assets (in millions of dollars)of 71 companies.The square root re-expression of assets is also given.In the square root re-expression,what does the value 45 actually indicate about the company's assets?

Here is the boxplot and an ogive of the distribution of students marks on their statistics test. Write a few sentences describing this distribution.