Question 1

If a frequency distribution is shown in a bar graph, what scale was used to measure the scores?
A) Nominal only
B) Nominal or ordinal
C) Ratio only
D) Interval or ratio

Accepted Answer

Bar graphs can represent data that are nominal (categories without a natural order) or ordinal (categories with a natural order), but they do not necessarily imply interval or ratio level measurements, which are typically represented with histograms.

Question 2

What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?
A) A bar graph
B) A histogram
C) A polygon
D) A line graph

Accepted Answer

A bar graph shows the frequencies as bars that are separated by spaces. A histogram also shows bars, but without any spaces between them, and is typically used for data that has been grouped into intervals. A polygon and line graph both show the trend of the data over time or some other continuous variable.

Question 3

If a distribution of numerical scores contains one or two extremely high values, compared to the rest of the scores, which measure of central tendency would produce the most representative value?
A) The mean
B) The median
C) The mode
D) The standard deviation

Accepted Answer

The median is the best measure of central tendency when a distribution contains extreme values because it is not affected by outliers. The mean is not recommended in this situation as it can be skewed by extreme values, while the mode is not useful for representing extreme values. The standard deviation is a measure of variability and does not represent central tendency.

Question 4

A researcher has measured self-esteem for a sample of 40 first-grade children. The researcher would like to divide the children into two equal-sized groups consisting of the high self-esteem kids and the low self-esteem kids. Which statistical measure will identify the correct score to serve as the boundary between the high and the low self-esteem groups?
A) The mean
B) The median
C) The mode
D) The standard deviation

Accepted Answer

The median is the statistical measure that divides a dataset into two equal halves. In this case, it will serve as the boundary between the high self-esteem kids and the low self-esteem kids, ensuring each group has an equal number of children.

Question 5

To construct a frequency distribution graph displaying a set of scores that were measured on an interval or a ratio scale, you should use a ____.
A) histogram
B) line graph
C) bar graph
D) scatter plot

Accepted Answer

A histogram is the best choice for displaying a frequency distribution graph for scores measured on interval or ratio scales. Histograms display data in a bar-like format, where the bar height represents the frequency of scores in a given interval. This is ideal for interval and ratio data because it allows for continuous data to be grouped together in intervals and displayed in a visual format that is easy to interpret. Line graphs are better suited for showing trends over time, bar graphs are better suited for categorical data, and scatter plots are better suited for displaying the relationship between two variables.

Question 6

Which general category of statistical methods is intended to answer questions about populations by using sample data?
A) Parameters
B) Statistics
C) Descriptive statistics
D) Inferential statistics

Accepted Answer

Inferential statistics are intended to answer questions about populations by using sample data. Parameters are numerical summaries of populations and statistics are numerical summaries of sample data. Descriptive statistics are used to summarize and describe characteristics of a data set, but do not make inferences about a larger population.

Question 7

Statistical techniques that summarize, organize, and simplify data are best classified as ____ statistics.
A) population
B) sample
C) descriptive
D) inferential

Accepted Answer

Descriptive statistics are used to summarize, organize, and simplify data by providing measures of central tendency and measures of variability. They do not involve making inferences or generalizations beyond the data being analyzed.

Question 8

A researcher records the change in weight (gain or loss) during the first semester of college for each individual in a group of 25 freshmen, and calculates the average change in weight. The average is an example of a ____.
A) parameter
B) statistic
C) variable
D) constant

Accepted Answer

The average change in weight calculated from the sample of 25 freshmen is a statistic because it is a numerical summary of the sample data. A parameter would be a numerical summary of the population data, which is not given in this scenario. Variable refers to the characteristic being measured (change in weight), and constant refers to a value that does not change.

Question 9

For scores measured on a nominal scale of measurement (e.g., job classification), which measure of central tendency is appropriate?
A) Mean
B) Median
C) Mode
D) Standard deviation

Accepted Answer

For scores measured on a nominal scale, the mode is the only appropriate measure of central tendency as it is the only one that can be computed for this type of data. The mean and median require data to be measured on an interval or ratio scale where it makes sense to calculate the average or midpoint. The standard deviation is a measure of variability and also requires data to be measured on an interval or ratio scale.

Question 10

A study with 50 research participants has a degree of freedom of ________.
A) 5
B) 25
C) 49
D) 51

Accepted Answer

The degree of freedom for a sample is calculated as the sample size minus 1. Therefore, the degree of freedom for a sample of 50 participants would be 50-1=49. Choice C is the correct answer.

Question 11

The weights of a group of patients in a weight loss program range from 185 to 312. A doctor constructs a frequency distribution graph showing the number of children for each of the six age groups. What kind of graph would be appropriate for this distribution?
A) A pie chart
B) A histogram
C) A bar graph
D) A scatter plot

Accepted Answer

A histogram would be appropriate for this distribution since it is a continuous variable (weights) that can be grouped into intervals (age groups). A pie chart would not be appropriate since there are no categories to compare and a scatter plot would not be appropriate since there is no correlation being examined. A bar graph could work, but a histogram would display the continuous nature of the variable better.

Question 12

What is the definition of variance?
A) The sum of the scores divided by the number of scores
B) The average distance from the mean
C) The square root of the average distance from the mean
D) The average squared distance from the mean

Accepted Answer

Variance is defined as the average squared distance from the mean. It is calculated by taking the sum of the squared differences between each score and the mean, divided by the total number of scores.

Question 13

The concept of degrees of freedom is associated with the ____.
A) mean for a sample
B) mean for a population
C) variance for a sample
D) variance for a population

Accepted Answer

Degrees of freedom are associated with variance, specifically the variance for a sample. It refers to the number of independent observations available for calculating the sample variance. The formula for calculating the sample variance involves dividing the sum of squared deviations by the degrees of freedom. The degrees of freedom for a sample is equal to n-1, where n is the sample size.

Question 14

A researcher uses an anonymous survey to investigate the drinking habits of American college students. Based on the set of 56 surveys that were completed and returned, the researcher finds that these students consume an average of four drinks each week. For this study, the average of four drinks is an example of a(n) ____.
A) parameter
B) statistic
C) population
D) sample

Accepted Answer

The average of four drinks is a statistic because it is based on the sample of 56 surveys that were completed and returned. It cannot be a parameter because parameters refer to characteristics of the entire population, which is not known in this study. Population refers to the entire group of individuals that the researcher is interested in, which could be American college students in general, but again, the characteristics of this population are not known in this study. Sample refers to the subset of the population that was studied, which in this case is the 56 surveys that were completed and returned.

Question 15

A researcher is interested in the anxiety levels among patients in a nursing home. The entire set of patients living in the nursing home is an example of a ____.
A) statistic
B) parameter
C) sample
D) population

Accepted Answer

The entire set of patients living in the nursing home represents the population of interest for the researcher.

Question 16

Where is a score of X = 45 located in a distribution with a mean of 40 and a standard deviation of 12?
A) Slightly above average
B) Far above average
C) Slightly below average
D) Far below average

Accepted Answer

A score of X = 45 is slightly above the mean of 40. Given the standard deviation is 12, a difference of 5 (45 - 40) is less than half a standard deviation, making it slightly above average but not far above.

Question 17

A researcher is interested in the sleeping habits of students at the local state college. The average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a ____.
A) statistic
B) parameter
C) sample
D) population

Accepted Answer

A parameter is a characteristic of a population, and in this scenario, the average number of hours spent sleeping each night for all students at the college is a characteristic of the population. A statistic, on the other hand, is a characteristic of a sample, which is a smaller subset of the population. A sample refers to a selected group of individuals, and it is not specified whether the researcher is looking at a specific sample or the entire population of students at the college. Therefore, the best answer is B, parameter.

Question 18

A researcher studies a group of 25 preschool children in order to answer questions about the entire population of preschool children. What general categories of statistical techniques will this researcher be using?
A) Parameters
B) Statistics
C) Descriptive statistics
D) Inferential statistics

Accepted Answer

The researcher will be using inferential statistics because they are using a sample (25 preschool children) to make inferences about the entire population of preschool children. Parameters refer to numerical measures of the population (not the sample), statistics refer to numerical measures of the sample, and descriptive statistics refer to methods used to summarize and describe the data (which could be used in conjunction with inferential statistics).

Question 19

It is possible for a distribution of scores to have more than one ____.
A) mean
B) median
C) mode
D) range

Accepted Answer

A distribution can have more than one mode if there are multiple values that occur with equal frequency. For example, in a bimodal distribution, there are two modes. The mean and median cannot have multiple values unless the data is skewed or has outliers. The range is simply the difference between the highest and lowest values and cannot have multiple values.

Question 20

A characteristic, usually a numerical value that describes a sample, is called a ____.
A) parameter
B) statistic
C) variable
D) constant

Accepted Answer

A statistic is a measure that describes a sample. Parameters, on the other hand, are measures that describe a population. Variables refer to the characteristics being measured, and constants are values that do not change.

Quiz 15: Statistical Evaluation of Data

If a frequency distribution is shown in a bar graph, what scale was used to measure the scores?

What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?

If a distribution of numerical scores contains one or two extremely high values, compared to the rest of the scores, which measure of central tendency would produce the most representative value?

To construct a frequency distribution graph displaying a set of scores that were measured on an interval or a ratio scale, you should use a ____.

Which general category of statistical methods is intended to answer questions about populations by using sample data?

Statistical techniques that summarize, organize, and simplify data are best classified as ____ statistics.

A researcher records the change in weight (gain or loss) during the first semester of college for each individual in a group of 25 freshmen, and calculates the average change in weight. The average is an example of a ____.

For scores measured on a nominal scale of measurement (e.g., job classification) , which measure of central tendency is appropriate?

A study with 50 research participants has a degree of freedom of ________.

The weights of a group of patients in a weight loss program range from 185 to 312. A doctor constructs a frequency distribution graph showing the number of children for each of the six age groups. What kind of graph would be appropriate for this distribution?

What is the definition of variance?

The concept of degrees of freedom is associated with the ____.

A researcher is interested in the anxiety levels among patients in a nursing home. The entire set of patients living in the nursing home is an example of a ____.

Where is a score of X = 45 located in a distribution with a mean of 40 and a standard deviation of 12?

A researcher is interested in the sleeping habits of students at the local state college. The average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a ____.

A researcher studies a group of 25 preschool children in order to answer questions about the entire population of preschool children. What general categories of statistical techniques will this researcher be using?

It is possible for a distribution of scores to have more than one ____.

A characteristic, usually a numerical value that describes a sample, is called a ____.