STAT Chapter 3

The distribution of a variable refers to the way its values are

spread over all possible values

How many columns does a frequency table typically have?

2

Determine whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). The explanation is more important than the answer. The third category in a frequency table has a cumulative frequency of 150. Choose the correct answer below. A: The statement makes sense. Even though no details are​ given, it is possible for the sum of the frequencies for the first three categories in a table to be​ 150, or any other whole number. B: The statement does not make sense. Even though no details are​ given, it is impossible for the proportion or percent of the frequency in the third category to be 150 times the total frequency. The proportion must fall between 0 and​ 1, inclusive. C: The statement makes sense. Even though no details are​ given, it is possible for the sum of the frequencies for the last three categories in a table to be​ 150, or any other whole number. D:The statement makes sense. Even though no details are​ given, it is possible for each of the first three categories to have a frequency of​ 150, or any other whole number

A

What should be included when making a graph of a​ distribution? A: A title​ and/or caption, scales and titles for the axes B: A title​ and/or caption, scales and titles for the​ axes, and a legend if more than one data set is shown on the graph C: A title​ and/or caption, scales and titles for the​ axes, a description of the type of graph​ used, and a legend D: A title​ and/or caption, scales and titles for the​ axes, and signature noting the creator

B

What is a frequency​ table? How does it show categories and​ frequencies? Choose the correct answer: A: A frequency table is used to display qualitative data. It uses wedges in a circle to represent the relative frequency of each​ category, which is the number of data values in the category. The size of each wedge is proportional to the relative frequency of the category it represents. B: A frequency table is used to display qualitative data. It uses a set of bars to represent the frequency of each​ category, which is the number of data values in the category. C: A frequency table has two columns. The first column lists all of the categories of data. The second column lists the frequency of each​ category, which is the number of data values in the category. D:A frequency table has two columns. The first column lists all of the categories of data. The second column lists the frequency of each​ category, which is the number of data values in the category and all preceding categories.

C

bar graph for quantitative data

histogram

number of data values in that category and all preceding categories

cumulative frequency

What is the formula for calculating relative frequency?

frequency in category/total frequency

A bar graph in which the bars are arranged in frequency order

pareto chart

Bar graphs are commonly used for what kind of data?

qualitative

any proportion of the data values that fall in that category

relative frequency

Determine whether the statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). A quality control engineer wants to draw attention to the car parts that require repair most​ often, so she uses a Pareto chart to illustrate the frequencies of repairs for the various car parts. A: Does not make sense because the Pareto chart puts the bars in order of frequency and therefore will make it hard to see which repairs occur most often. B: Makes sense because the Pareto chart puts the bars in order of frequency and therefore will make it easy to see which repairs occur most often. C: Makes sense because the Pareto chart can show how long a part will last before needing repair. D: Does not make sense because a​ time-series graph would better show the time a part will last before needing repair

B

Decide whether the following statements makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. I made a frequency table with two​ columns, one labeled​ "State" and one labeled​ "State Capitol." Choose the correct answer below. A: The statement makes sense. In a frequency​ table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property. B:The statement makes sense. The set of states is clearly defined and each state has a clearly defined capitol. C: The statement does not make sense. In a frequency​ table, each category must have a frequency greater than 1. Because each state has exactly one​ capitol, each category in the table described in the given statement would have frequency 1. D: The statement does not make sense. In a frequency​ table, one of the columns lists the frequency of each​ category, which is the number of data values in the category. The table described in the given statement does not have this column.

D

Explain how a graph that shows percentage change can show descending bars​ (or a descending​ line) even when the variable of interest is increasing. Choose the correct answer below. A: The horizontal axis on the graph has an opposite direction. B: The vertical axis on the graph has an opposite direction. C: The horizontal axis on the graph represents unequal intervals such that the​ drop-off means only the actual value of the variable rises by smaller amounts. D: The vertical axis on the graph represents a percentage change such that the​ drop-off means only the actual value of the variable rises by smaller amounts.

D

The following describes a data set but does not give actual data. For the data​ set, state the type of graphic that you believe would be most appropriate for displaying the​ data, if they were available. Explain your choice. The number of​ full-time students enrolled in colleges in each year since 1990. A: A​ time-series graph would be effective in showing the number of​ full-time college students since 1990 is a time. B: A​ time-series graph would be effective in showing any trend in the number of​ full-time college students since 1990 as the data represent changes over a period of time. C: A Pareto chart would be effective in showing the number of​ full-time college students since 1990 because the graph would be arranged from high to low D: A pie chart would be effective in showing the number of​ full-time college students since 1990 as the data can easily be seen.

B

A distribution is which of the​ following? A: A method of assigning the data to different groups or bins B: A measure of the way the values of a variable are spread over all possible values that can be summarized with a number C: The way the values of a variable are spread over all possible values that can be summarized with a table or a graph D: The range of all possible values that a variable can be assigned

C

Weekly instruction time for a school student in one country is 23.5 hours compared to 29.6 hours in another country. Is the difference​ meaningful? How could a graph be constructed so that the difference is greatly​ exaggerated? Choose the correct answer below. A: The difference of 6.1 hours is meaningful. To exaggerate the​ difference, use a bar graph and arrange the countries in ascending or descending order of the number of hours. B: The difference of 6.1 hours is not meaningful. To exaggerate the​ difference, use a bar graph with a vertical scale from 0 to 100 hours. C: The difference of 6.1 hours is meaningful. To exaggerate the​ difference, use a bar graph and start the vertical scale at 20 hours. D: The difference of 6.1 hours is not meaningful. To exaggerate the​ difference, use a percent change graph of the differences in the number of hours between the countries.

C