Organizing Data

Identify an important reason for grouping data.

Do the concepts of class limits, marks, cutpoints, and midpoints make sense for qualitative data? Explain your answer.

State three of the most important guidelines in choosing the classes for grouping a quantitative data set.

With regard to grouping quantitative data into classes in which each class represents a range of possible values, we discussed two methods for depicting the classes. Identify the two methods and explain the relative advantages and disadvantages of each method.

Use single-value grouping.

Use single-value grouping.

Use single-value grouping.

Use single-value grouping.

Use limit grouping with the first class of $0-9$ and a class width of $10$.

Use limit grouping with the first class of $0-4$ and a class width of $5$.

Use limit grouping with the first class of $30-36$ and a class width of $7$.

Use limit grouping with the first class of $50-59$ and a class width of $10$.

Use cutpoint grouping with a first class of $10$ -under $15$.

Use cutpoint grouping with a first class of $40$ -under $46$.

For quantitative data, we examined three types of grouping: single-value grouping, limit grouping, and cut point grouping. For each type of data given, decide which of these three grouping types is usually best, Explain your answers.

a. Continuous data displayed to one or more decimal places

b. Discrete data in which there are relatively few distinct observations

We used slightly different methods for determining the "middle" of a class with limit grouping and cut point grouping. Identify the methods and the corresponding terminologies.

Explain the difference between a frequency histogram and a relative-frequency histogram.

Explain the advantages and disadvantages of frequency histograms versus frequency distributions.

For data that are grouped in classes based on more than a single value, lower-class limits (or cut points) are used on the horizontal axis of a histogram for depicting the classes. Classmarks (or midpoints) can also be used, in which case each bar is centered over the mark (or midpoint) of the class it represents. Explain the advantages and disadvantages of each method.

Discuss the relative advantages and disadvantages of stem-and leaf diagrams versus frequency histograms.

Suppose that you have a data set that contains a large number of observations. Which graphical display is generally preferable; a histogram or a stem-and-leaf diagram? Explain your answer.

Suppose that you have constructed a stem-and-leaf diagram and discover that it is only moderately useful because there are too few stems. How can you remedy the problem?

Number of Bedrooms. The number of bedrooms per single-family dwelling.

In this case, decide which type of grouping (single-value, limit, or cutpoint is probably the best.

Ages of Householders. The ages of householders, given as a whole number

In this case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best.

Sleep Aids. The additional sleep, to the nearest tenth of an hour, was obtained by a sample of $100$ patients by using a particular brand of sleeping pill. In this case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best.

Number of Cars. The number of automobiles per family

In this case, decide which type of grouping (single-value, limit or cutpoint is probably the best.

Gas Mileage. The gas mileages, are rounded to the nearest number of miles per gallon, of all new car models. 

Giant Tarantulas: The carapace lengths, to the nearest hundredth of a millimeter, of a sample of $50$ giant tarantulas.

In each case, decide which type of grouping (single-value, limit or cutpoint is probably the best.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use single-value grouping.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use single-value grouping.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use single-value grouping.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use single-value grouping.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use limit grouping with a first class of $0-9$ and a class width of $10$.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use limit grouping with a first class of $0-4$ and a class width of $5$.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use limit grouping with a first class of $30-36$ and a class width of $7$.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use limit grouping with a first class of $50-59$ and a class width of $10$.

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use cutpoint grouping with a first class 10-under 15.

We have presented some quantitative data sets and specified a grouping method for practicing the concepts.

Part (a): Determine a frequency distribution.

Part (b): Obtain a relative-frequency distribution.

Part (c): Construct a frequency histogram based on your result from part (a).

Part (d): Construct a relative frequency histogram based on your result from part (b).

Use cutpoint grouping with a first class of 40-under 46.

Cottonmouth Litter Size. In the paper "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. 29, No. 3, PP. 391-398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 24 female cottonmouths in Florida yielded the following data on number of young per litter. Use single-value grouping.

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result from part (b).

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result from part (b).

The U.S. Energy Information Administration collects data on residential energy consumption and expenditures. Results are published in the document

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result from part (b).

Use cutpoint grouping with a first-class midpoint of $0.5$ and a class width of $1$.

Use cutpoint grouping with the first cutpoint of $25$ and a class width of $3$.

Number of Siblings. Professor Weiss asked his introductory statistics students to state how many siblings they have. The responses are shown in the following table. Use single-value grouping.

Household Size. The U.S. Census Bureau conducts nationwide surveys on the characteristics of U.S. households and publishes the results in Current Population Reports. Following are data on the number of people per household for a sample of $40$ households. Use single-value grouping.

Construct a dot plot for the data.

Construct a dot plot for the given data.

Construct a dot plot for the given data.

Construct a dot plot for the given data.

Construct a stem-and-leaf diagram for the data, using one line per stem.