AP Statistics Chapter 1 Quiz

Questions and Answers

Which of the following statements is NOT true?

The first quartile is equivalent to the twenty-fifth percentile.

The median is always greater than the mean. (correct)

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

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

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

Which of the following statements is correct?

Your friend must not have followed the diet correctly, since she did not lose weight.

In order for the study to be correct, we must now add your friend's results to those of the study and recompute the new average.

Since your friend did not lose weight, the report must not be correct.

The report gives only the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results. (correct)

Your friend is an outlier.

When converted to °F, the mean and standard deviation are (°F = °C(1.8) + 32):

97.7, 0.97

97.7, 0.30

97.7, 0.54 (correct)

97.7, 1.80

97.7, 32

If a four-year-old child enters the room, which statement is true?

The mean age will stay the same but the variance will decrease. Signup and view all the answers

If a distribution is skewed to the right, which of the following is true?

The mean must be greater than the median. Signup and view all the answers

Which describes how the company's mean and median salaries would change if the owner gives himself a $30,000 raise?

The mean would increase by $5,000 and the median would not change. Signup and view all the answers

After correcting the maximum value from 40 to 50, which statement is true?

The median remains the same, but the mean is increased. Signup and view all the answers

Approximately how many students had scores between 35 and 61?

95 Signup and view all the answers

Which of the following best describes the variables measured in the survey?

Three categorical variables and two quantitative variables Signup and view all the answers

What must be true about the mean speed of all vehicles on the turnpike?

It could be any number between 64 and 68 miles per hour. Signup and view all the answers

What is a correct interpretation of the standard deviation of the birth weight of infants?

The distance between the weight of each infant born in April and the mean weight was, on average, about 10.2 oz. Signup and view all the answers

What is the median age of the remaining four people after one leaves?

Cannot be determined from the information given Signup and view all the answers

Study Notes

Understanding Statistics Concepts

Symmetric distributions have equal mean and median; incorrect to state median is always greater than mean.
The first quartile represents the 25th percentile in a data set.
Average weight loss reported in a study does not guarantee all participants experienced loss; individual experiences may vary even if the average is accurate.

Temperature Conversion

Mean body temperature: 36.5°C converts to 97.7°F, with a standard deviation of 0.3°C converting to 0.54°F.

Age Statistics

Adding a four-year-old child to a group of ages 3, 4, and 5 keeps the mean age constant while reducing variance due to the repetition of the four-year age.

Skewness in Distributions

In a right-skewed distribution, the mean is greater than the median, reflecting the influence of higher outlier values.

Salary Implications

A significant salary raise for the owner of a small company affects the mean salary by increasing it, while the median remains unchanged due to no change in the number of employees at lower salary levels.

Correcting Data Errors

Adjusting the maximum value from 40 to 50 in a sample affects the mean (increases it) but does not alter the median.

Five-Number Summary

Out of 380 students, approximately 95 scored between the 35th and 61st percentiles based on the five-number summary.

Variable Types in Surveys

Variables in a high-school survey include three categorical (gender, favorite subject, college plans) and two quantitative (age, years at current address).

Vehicle Speed Averages

Mean speeds of vehicles across two lane types suggest overall speed must lie between the two given means (64 mph to 68 mph).

Standard Deviation Interpretation

The standard deviation indicates variability; in this case, the average infant's birth weight differs from the mean by about 10.2 oz.

Median Age Calculation

Removal of an individual with a higher age from the group can lead to an indeterminate median for the remaining individuals without knowing their ages.

Description

Test your understanding of key concepts in the first chapter of AP Statistics. This multiple choice quiz covers fundamental statistical ideas including distributions, quartiles, and measures of central tendency. Perfect for revision or to check your knowledge.