Sample
What term describes all the elements of interest in a study that share one or more qualities?
Population
A researcher codes region as Northeast = 1, South = 2, Midwest = 3, and West = 4.
Why would calculating the mean of these codes be meaningless?
Region is nominal. The numbers are labels rather than meaningful quantities or ranks.
What does the height of a bar in a frequency histogram represent?
The number of observations within a particular value or class interval.
What measure of central tendency indicates the most frequently occurring value?
The mode.
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarize and present the data that have been collected, while inferential statistics use sample data to estimate or draw conclusions about a larger population.
Consider the response scale:
1 = Strongly disagree
2 = Disagree
3 = Neutral
4 = Agree
5 = Strongly agree
What type of variable is this, nominal or ordinal? And why?
Ordinal, because its categories have a meaningful order.
What proportion of students earned a score of at least 80?
40%. Add the relative frequencies for scores from 80–89 and 90 or above: 0.28 + 0.12 = 0.40.
For the ordered data 3, 3, 5, 6, and 8, what is the median?
5
A survey of 1,500 U.S. adults finds that 62% support a policy. Identify the statistic and the population parameter it is intended to estimate.
The statistic is the sample proportion, 62%. It estimates the unknown proportion of all U.S. adults who support the policy.
Why is the number of children in a household considered a discrete rather than a continuous variable?
It is a count that can take only distinct whole-number values.
What charts are most appropriate to display single-variable qualitative data?
circle graphs (pie diagrams) and bar graphs
Two classes have the same mean exam score. Class A has a standard deviation of 3, while Class B has a standard deviation of 15. What does this tell you?
Class A’s scores are more tightly clustered around the mean; Class B’s scores are more dispersed.
To estimate support for a policy among students at a university, researchers draw three random samples:
Sample A: 58%
Sample B: 61%
Sample C: 59%
Why do the estimated support rates differ even though all three samples were drawn from the same population?
Sampling variability causes statistics to vary from one random sample to another.
One survey asks respondents to report their exact household income, while another asks them to select an income range. How does the level of measurement differ between the two surveys?
Exact household income is a quantitative, ratio-scaled variable. Income ranges form an ordinal variable because the categories are ordered, but exact differences between respondents cannot be determined.
What proportion of scores falls from 70 up to,but not including, 90?
63%. Subtract the cumulative proportion below 70 from the cumulative proportion below 90: 0.88 − 0.25 = 0.63.
Why is the standard deviation generally easier to interpret than the variance?
The standard deviation is expressed in the original units of the data, while the variance is expressed in squared units.
Consider the following sampling process:
Target population -> Imperfect sampling frame -> Random sample
Why might the resulting sample still be biased, even if individuals are selected randomly?
Random selection cannot represent population members who are missing from the sampling frame.
Political participation is measured in three ways: whether a person voted, the number of political activities they completed, and whether their participation was low, moderate, or high. How is the variable measured in each case?
Voting status is nominal, the number of activities is quantitative and discrete, and the participation categories are ordinal.
The groups have the same median. What important difference does the table reveal?
The centers are similar, but Group B has much greater variability and more extreme values on both sides of the median.
What is the mean number of children per family?
The mean is 2.15 children.