AP Stats Ch 1 Review

​AP Statistics Ch. 1 Review

Do you know all the important information?

Can you give the best answer to an FRQ?​

Ch. 1: Data Analysis​

Multiple Choice

You measure the age (years), weight (pounds), and breed (beagle, golden retriever, pug, or terrier) of 200 dogs. How many categorical variables did you measure?

• 1

• 2

• 3

• 4

Multiple Choice

You measure the age (years), weight (pounds), and breed (beagle, golden retriever, pug, or terrier) of 200 dogs. What are the individuals?

• the ages

• the weights

• the breeds

• the dogs

Multiple Choice

A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation. (Apparently this town has no one who is comfortable identifying as non-binary.) The proportion of males that are registered as Democrats is:

• 300

• 30

• 0.33

• 0.30

• 0.15

Marginal relative frequencies take a row or column total and divide by the grand total of the table. ​

​Some text here about the topic of discussion.

Marginal Relative Frequency

Some questions about marginal relative frequency:

• What percent of the town are Democrats?

  • (300+600)/ 2000 = 0.45 = 45%​

• What percent of the town are Male?​

  • (300+500+200) / 2000 = ​0.5 = 50%

Conditional relative frequencies focus on only part of the table: only one row or one column.

Then the individual cell is divided by the row or column total.​

​Some text here about the topic of discussion.

Conditional Relative Frequencies

Some questions that can be answered with conditional relative frequencies are:

• What percent of men are Democrats?

• What proportion of registered ​Republicans are women?

Joint relative frequencies are concerned with two conditions. They are calculated by taking the individual cell and dividing by the grand total.

​Some text here about the topic of discussion.

Joint relative frequencies

Some questions that can be answered with joint relative conditions are:

• ​What percent of the town are women who are registered Republicans?

• What percent are Democrats and men?

Multiple Choice

The following two-way table displays data for 219 students who responded to a survey. What percent of the students who responded were Facebook users?

• 67.6%

• 35.6%

• 52.7%

• 148

Multiple Choice

The bar graph displays data on the percent of people in several age groups who attended a movie in the past 12 months.

Which of the following statements is supported by the bar chart?

• The greatest number of movie-goers questioned were 18-24.

• The relative frequency of movie-goers above 65 was 50%.

• 18-24 year-olds had the greatest relative frequency of attending movies.

• The majority of movie audiences are between 18 and 24 years-old.

Multiple Choice

Is there a relationship between Facebook use and age among college students? The following two-way table displays data for the 219 students who responded to the survey. Their ages are represented in the columns. Which of the following is the best evidence that there is an association between the age of a college student and their Facebook use?

• Only 4 of the younger students didn't use Facebook.

• It isn't possible to identify an association because there are different amounts of students at each age range.

• Fewer older students were Facebook users than younger students.

• A higher percentage of younger students (95%) than older students (31%) are Facebook users.

• The combination of using Facebook and being young occurred more often (78 times) than any other combination of outcomes.

If there is no association between two categorical variables, then the presence of one will not affect the relative frequency of the other.

No Association

If there is an association between two categorical variables, then the presence of one will influence the relative frequency of the other.

Association

​Association or No Association

For example, 10% of Freshmen, Sophomores, Juniors and Seniors are left-handed. There is no association between class level and handedness.

Multiple Choice

The following relative frequency table shows the political party affiliation for a sample of 500 people in a certain town. Which of the following statements is supported by the table?

• There is no association between age and political affiliation because the same proportions of people are Republican, Democrat or Independent.

• There is no association between age and political affiliation because the same number of people in each group are independents.

• There is an association between age and political affiliation because there are approximately the same number of individuals in each age group.

• There is an association because there are different proportions of people in each political party depending on their age.

Multiple Choice

When drawing a histogram it is important to

• have a separate class interval for each observation to get the most informative plot.

• make sure the heights of the bars exceed the widths of the class intervals so that the bars are true rectangles.

• label the vertical axis so the reader can determine the counts or percent in each class interval.

• leave large gaps between bars. This allows room for comments.

• scale the vertical axis according to the variable whose distribution you are displaying.

Multiple Choice

Realtors collect data in order to serve their clients more effectively. In a recent week, data on the age of all homes sold in a particular area were collected and displayed on this histogram. If the interval width were increased from 5 to 10 years, which of the following must not change on the new histogram?

• the heights of the bars

• the widths of the bars

• the number of bars

• the sum of the frequencies

• the shape of the distribution

Multiple Choice

For a physics course containing 10 students, the maximum point total for the quarter was 200. The point totals for the 10 students are given in the stemplot below. Which of the following statements is NOT true?

• In a symmetric distribution, the mean and the median are equal.

• About fifty percent of the scores in a distribution are between the first and third quartiles.

• In a symmetric distribution, the median is halfway between the first and third quartiles.

• The median is always greater than the mean.

• The range is the difference between the largest and the smallest observation in the data set.

Multiple Choice

A set of data has a mean that is much larger than the median. Which of the following statements is most consistent with this information?

• the distribution is symmetric

• the distribution is skewed left

• the distribution is skewed right

• the distribution is bimodal.

• the data set probably has a few low outliers.

Multiple Choice

This is a boxplot of the birth weights (in ounces) of a sample of 160 infants born in a local hospital. About 40 of the births weights were below

• 92 ounces

• 102 ounces

• 112 ounces

• 122 ounces

• 132 ounces

​What if you didn't take the square root to get the standard deviation?

Standard deviation (for a sample)

Then you'd have the variance!

It's basically just the standard deviation before taking the square root. Or, you can find it by squaring the standard deviation.

It won't be on the test, but here's a question to practice calculating the standard deviation and then square it to find the variance. ​

​​Variance - another measure of spread

Multiple Choice

A sample of production records for an automobile manufacturer shows the following figures for production per shift:

705 700 690 705

The variance of the sample is approximately

• 8.66

• 7.07

• 75.00

• 50.00

• 20.00

Multiple Choice

A policeman records the speeds of cars on a certain section of roadway with a radar gun. The histogram below shows the distribution of speeds for 251 cars. Which of the following measures of center and spread would be the best ones to use when summarizing these data?

• mean and interquartile range

• mean and standard deviation

• median and range

• median and standard deviation

• median and interquartile range

Multiple Choice

Andrez claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the

mean and the standard deviation. Is Andrez's claim correct?

• Yes, both the mean and median are likely to change greatly. They are not resistant to outliers.

• No, only the median is likely to change greatly.

• No, neither the mean nor the standard deviation are likely to change greatly.

• There is not enough information to determine if the mean or the median is likely to change greatly.

-Love, Ms. Donalek

​I'm out of time for today, so please also review the FRQ practice in the book on p. 87.