Question 1

In a sample of 1000 students in a university, 125, or 12.5%, are biology majors. The 12.5% is an example of statistical inference.

Accepted Answer

The 12.5% represents a sample proportion, which is a descriptive statistic, not a result of statistical inference.

Question 2

If the manager of a grocery store wishes to display the sales trend, which of the following is the most effective type of graph to use?

Accepted Answer

A line chart is the most effective type of graph to display sales trends as it shows the changes in sales over time. It allows the manager to track the ups and downs of sales and identify any patterns or trends that may be occurring. A bar chart would only display sales figures for a particular period, while a pie chart would be better suited for displaying proportions of different categories. A histogram is used to display distributions of data and would not be appropriate for displaying sales trends.

Question 3

Persons or objects that have characteristics of interest to statisticians are called variables.

Accepted Answer

Persons or objects that have characteristics of interest to statisticians are called "units" or "observations," while the characteristics themselves are called "variables."

Question 4

A stem-and-leaf plot is used to display the distribution of which of the following kinds of data?

Accepted Answer

A stem-and-leaf plot is a visual representation used to display the distribution of quantitative data. The stems represent the first digit(s) of the data values and the leaves represent the remaining digits. This allows for easy identification of the frequency of values within certain ranges or intervals. Therefore, stem-and-leaf plots are not appropriate for qualitative data or two qualitative variables, as they do not involve numerical values. Additionally, while two quantitative variables can be displayed together using a scatterplot, a stem-and-leaf plot is specific to a single variable.

Question 5

A variable that is normally described in words, rather than numerically presented, is a qualitative variable.

Accepted Answer

A qualitative variable is one that describes a quality or characteristic and is typically presented through words or categories, rather than numerical values. Examples include gender, eye color, and political affiliation.

Question 6

A variable is a characteristic that changes over time, and/or varies for different individuals or objects under consideration. An experimental unit is the individual or object on which a variable is measured.

Accepted Answer

This is a correct statement. A variable can vary between different individuals or objects, and an experimental unit is the individual or object on which a variable is measured.

Question 7

Suppose you are given a graphical portrayal of a relative frequency distribution of continuous quantitative data with the following characteristics. The lower and upper limits of the data classes are identified by tick marks on a horizontal axis. The corresponding relative class frequencies are represented by the areas of vertical rectangles connected to each other and positioned on top of each of these class intervals. What is such a graphical presentation called?

Accepted Answer

The graphical portrayal described is a relative frequency histogram. This is because it displays continuous quantitative data with class intervals identified by tick marks on a horizontal axis and uses vertical rectangles to represent the corresponding relative frequencies of each class. A stacked bar chart would show multiple bars stacked on top of each other to show the composition of each bar, a Pareto chart would show a bar graph with the bars ordered by their heights, and a pictogram would use pictures or symbols to represent data values.

Question 8

Individual observations within each class may be found in a frequency distribution.

Accepted Answer

A frequency distribution summarizes the data by reporting the number of observations within each class or category, but it does not list individual observations.

Question 9

Which of the following should generally NOT be used when constructing a relative frequency histogram?

Accepted Answer

Open-ended classes should generally not be used when constructing a relative frequency histogram because they could cause inaccuracies in calculating the relative frequencies for each class. This is because the exact boundaries of an open-ended class are not defined, making it difficult to determine the total number of observations that fall within it. Instead, closed-ended (bounded) classes are typically used because they have clearly defined boundaries and are easier to work with when building a relative frequency histogram.

Question 10

How many classes should generally be used when constructing a relative frequency histogram?

Accepted Answer

The optimal number of classes that should be used when constructing a relative frequency histogram is generally between 5 and 12 classes. This is because having too few classes may result in important features of the data being overlooked, while having too many classes may result in noise in the data being accentuated, leading to less meaningful insights. Therefore, a range of 5 to 12 classes is considered the best choice for constructing an informative and accurate relative frequency histogram.

Question 11

Statistical inference is the process of making an estimate, prediction, or decision about a population based on sample data.

Accepted Answer

Statistical inference involves using sample data to draw conclusions about a larger population. These conclusions may take the form of an estimate (such as the mean or proportion of the population), a prediction (such as forecasting future values), or a decision (such as whether to accept or reject a hypothesis). The process typically involves using probability theory and statistical methods to quantify the uncertainty or variability inherent in the data and the conclusions drawn from it.

Question 12

A qualitative variable about which observations can be made in only two categories is a bivariate data set.

Accepted Answer

A bivariate data set is a data set that involves two different variables. A qualitative variable with two categories would be considered a univariate data set.

Question 13

A branch of the statistics discipline that is used to develop and utilize techniques for properly making inferences about population characteristics based on information contained in a sample drawn from this population is called inferential statistics.

Accepted Answer

This is the definition of inferential statistics.

Question 14

Twenty-five percent of a sample of 200 professional tennis players indicated that their parents did not play tennis. This is an example of descriptive statistics, rather than inferential statistics.

Accepted Answer

This statement is describing a characteristic of a sample, rather than making a prediction or inference about a larger population. Therefore, it is an example of descriptive statistics.

Question 15

A histogram is a graphical device. What kind of data is it commonly used to display?

Accepted Answer

Histograms are commonly used to display quantitative data, such as the distribution of a set of continuous or discrete numerical values. The data is organized into intervals or “bins” on the x-axis and the frequency or proportion of data points falling into each interval is depicted by the height of bars on the y-axis. This provides a visual representation of the distribution of the data, including measures such as central tendency, variability, and skewness.

Question 16

A local cable system using a sample of 1000 subscribers estimates that 50% of its subscribers watch premium channels at least five times per week. This is an example of inferential statistics, as opposed to descriptive statistics.

Accepted Answer

Inferential statistics involves making predictions or inferences about a population based on a sample, which is what the cable system is doing by estimating the behavior of all subscribers from a sample of 1000.

Question 17

In the term "frequency distribution," frequency refers to the number of data values or measurements falling within each class.

Accepted Answer

This is correct, frequency in a frequency distribution refers to the number of data values or measurements falling within each class.

Question 18

Bar and pie charts are graphical techniques for qualitative data. The former focus the attention on the frequency of the occurrences of the categories; the latter emphasize the percentage of occurrences of each category.

Accepted Answer

Bar charts display the frequency of each category, while pie charts show the proportion or percentage of each category in relation to the whole.

Question 19

Which of the following might best be displayed using a bar chart?

Accepted Answer

Bar charts are best suited for displaying qualitative variables, which are categorical in nature.

Question 20

A branch of the statistics discipline that is used to develop and utilize techniques for effectively presenting numerical information is called inferential statistics.

Accepted Answer

Inferential statistics is actually used to analyze data and make inferences about a population based on a sample, rather than presenting numerical information. The branch of statistics that deals with presenting numerical information is known as descriptive statistics.

Quiz 1: Describing Data With Graphs