Question 1

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

Accepted Answer

Bar graphs are used for categorical data, which can be measured on a nominal or ordinal scale.

Question 2

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

Accepted Answer

Since nominal scales are not quantitative, and each value is assigned to categories without arbitrary numerical values, the mode is the only appropriate measure of central tendency there is.

Question 3

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

Accepted Answer

Degrees of freedom (df) are associated with the variance for a sample. It represents the number of values in the final calculation of a statistic (such as sample variance) that are free to vary. When calculating sample variance, some values are fixed because the sum of deviations from the mean is always zero. Therefore, the degrees of freedom are n-1, where n is the sample size, to reflect the fact that only n-1 values are free to vary.

Question 4

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?

Accepted Answer

The median is the middle value in a distribution, regardless of extreme values. Therefore, it is not influenced by any extreme values of the data, unlike the mean.

Question 5

If a set of scores has a mean of 45 and a standard deviation of 9,then the scores have a variance of ____.

Accepted Answer

Variance is the square of the standard deviation. Therefore, the variance is 9^2 = 81.

Question 6

What is the definition of variance?

Accepted Answer

Variance is defined as the average of squared differences from the mean. It is calculated by subtracting the mean from each score, squaring the difference, summing the squared differences, and dividing by the number of scores. Therefore, option D, i.e. the average squared distance from the mean is the correct answer.

Question 7

A researcher uses an anonymous survey to investigate the study habits of American college students.Based on the set of 56 surveys that were completed and returned,the researcher finds that these students spend an average of 4.1 hours each week working on course material outside of class.For this study,the average of 4.1 hours is an example of a(n)____.

Accepted Answer

The average of 4.1 hours is a calculation based on the data collected from the set of 56 surveys, making it a statistic, as it describes the characteristics of the sample, not the entire population of American college students.

Question 8

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

Accepted Answer

A parameter is a characteristic that describes a population, while a statistic is a characteristic that describes a sample. Therefore, since the question is referring to a characteristic that describes a sample, the best choice is B, which is a statistic. A variable is a characteristic that can take on different values, and a constant is a value that does not change.

Question 9

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

Accepted Answer

A score of X = 45 is slightly above average in this distribution. This is because the mean is 40, and a score of 45 is 5 points above the mean. Additionally, the standard deviation is 12, which means that a score of 45 is less than one standard deviation away from the mean.

Question 10

A researcher is interested in the sleeping habits of students at the local state college.The entire set of students enrolled at the college is an example of a ____.

Accepted Answer

The entire set of students enrolled at the college is the population, which is the complete group of individuals or objects that the researcher is interested in studying.

Question 11

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?

Accepted Answer

The median is the best choice to divide the children into two equal-sized groups because it represents the middle score when the data is ordered from lowest to highest. Since the sample size is even (40), the median will be the average of the 20th and 21st scores when the data is ordered. This will ensure that half of the children have high self-esteem scores and half have low self-esteem scores. The mean and standard deviation are affected by extreme scores and may not accurately represent the typical score in the sample. The mode is not relevant since we are not looking for the most common score, but rather the boundary between the two groups.

Question 12

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

Accepted Answer

The mode is the value that occurs most frequently in a distribution. It is possible for a distribution to have multiple modes if there are multiple values that occur with the same frequency. This is not the case for the mean or median, as they are numerical summaries of the distribution and can only have one value. The range is simply the difference between the highest and lowest values in the distribution and does not have multiple values.

Question 13

The ages of the children in a summer camp range from 7 to 12 years old.A counselor 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?

Accepted Answer

The answer of The ages of the children in a...

Question 14

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

Accepted Answer

Inferential statistics is used to make inferences or predictions about a population based on sample data. It involves analyzing and interpreting data and drawing conclusions or making predictions based on probability theory. It is different from descriptive statistics, which summarizes and describes the features of a sample or population, and from parameters which are characteristics of the population. Statistics, on the other hand, refers to numerical data or information derived from a sample or population.

Question 15

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

Accepted Answer

Descriptive statistics are used to summarize, organize, and simplify data. They include measures of central tendency (such as mean, median, and mode) and measures of variability (such as range, variance, and standard deviation). Descriptive statistics are used to describe the characteristics of a sample or population, without making any inferences about the larger population from which the sample was drawn.

Question 16

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?

Accepted Answer

The researcher will be using inferential statistics to make inferences about the entire population of preschool children based on the data collected from the sample of 25 children. This involves using statistical techniques such as hypothesis testing and confidence intervals to make predictions or draw conclusions about the population.

Question 17

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 ____.

Accepted Answer

The average change in weight is a statistic because it is based on a sample of 25 freshmen and is intended to estimate the average change in weight for the population of all freshmen at that college. A parameter would refer to the true average change in weight for the entire population, which is typically unknown and estimated using statistics. "Variable" refers to a characteristic that varies among individuals or objects in a population, and "constant" is a value that does not vary.

Question 18

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 ____.

Accepted Answer

A parameter is a measure that describes an entire population, in this case the entire set of students enrolled at the college.

Question 19

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

Accepted Answer

A bar graph displays the frequencies as bars that are separated by spaces. Histograms also use bars, but there are no spaces between them. Polygons and line graphs use lines to connect the data points.

Question 20

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 ____.

Accepted Answer

A histogram is the appropriate choice for constructing a frequency distribution graph for interval or ratio scale scores. Histograms display the distribution of continuous data by dividing the data into intervals or bins and plotting the frequency of scores in each interval as a vertical bar. This allows for a clear understanding of the pattern, shape, and central tendency of the data. Line graphs are used when the data is continuous and changes over time. Bar graphs are used when the data is categorical. Scatter plots are used when there are two continuous variables and one is the predictor of the other.

Quiz 15: Statistical Evaluation of Data.