Grouping and Displaying data to convey meaning

Here is a frequency distribution of the weight of 150 people who used a ski lift a certain day. Construct a histogram for these data.

1. What can you see from the histogram about the data that was not immediately apparent from the frequency distribution?
2. If each ski lift chair holds two people but is limited in total safe weight capacity to 400 pounds, what can the operator do to maximize the people capacity of the ski lift without exceeding the safe weight capacity of a chair? Do the data support your proposal?

Solution

Central Carolina Hospital has the following data representing weight in pounds at birth of 200 premature babies.

Construct an ogive that will help you answer these questions:

1. What was the approximate middle value in the original data set?
2. If premature babies under 3.0 pounds are normally kept in an incubator for several days as a precaution, about what percentage of Central’s premature babies will need an incubator?

Solution

Here is a frequency distribution of the length of phone calls made by 175 people during a Labor Day weekend.

Solution

Golden Acres is a homeowners' association that operates a trailer park outside Orlando, Florida, where retirees keep their winter homes.

Solution

Homer Willis, a fishing boat captain from Salter Path, North Carolina, believes that the break-even catch on his boats is 5,000 pounds per trip.

Solution

The Massachusetts Friends of Fish has the following data representing pollutants (in parts per million) at 150 sites in the state.

Solution

Before constructing a dam on the Colorado River, the U.S. Army Corps of Engineers performed a series of tests to measure the water flow past the proposed location of the dam. The results of the testing were used to construct the following frequency distribution:

1. Use the data given in the table to construct a “more-than” cumulative frequency distribution and ogive.
2. Use the data given in the table to construct a “less-than” cumulative frequency distribution and ogive.
3. Use your ogive to estimate what proportion of the flow occurs at less than 1,30thousands of gallons per minute.

Solution

Pamela Mason, a consultant for a small local brokerage firm, was attempting to design investment programs attractive to senior citizens. She knew that if potential customers could obtain a certain level of return, they would be willing to risk an investment, but below a certain level, they would be reluctant. From a group of 50 subjects, she obtained the following data regarding the various levels of return required for each subject to invest $1,000

1. Use the data given in the table to construct a “more-than” cumulative frequency distribution and ogive.
2. Use the data given in the table to construct a “less-than” cumulative frequency distribution and ogive.
3. Use your ogive to estimate what proportion of the flow occurs at less than 1,30thousands of gallons per minute.

Solution

At a newspaper office, the time required to set the entire front page in type was recorded for 50 days. The data, to the nearest tenth of a minute, are given below.

1. Arrange the data in an array from lowest to highest.
2. Construct a frequency distribution and a “less-than” cumulative frequency distribution from the data, using intervals of 0.8 minute.
3. Construct a frequency polygon from the data.
4. Construct a “less-than” ogive from the data.
5. From your ogive, estimate what percentage of the time the front page can be set in less than 24 minutes.

Solution

Chien-Ling Lee owns a CD store specializing in spoken-word recordings. Lee has 35 months of gross sales data, arranged as a frequency distribution.

1. Construct a relative frequency distribution.
2. Construct, on the same graph, a relative frequency histogram and a relative frequency polygon.

Solution