AP Statistics
Semester Review of Descriptive Statistics Unit
Video D: Discrete v. Continuous
1. Identify which variable [data] is discrete and which is continuous.
a) Weights of people
b) Readings of weights on an electronic scale reporting weights to the nearest tenth of a pound.
Video E: Measures of Central Tendency
1. Identify the mean, median, and mode of the following quiz scores. 10 points were possible.
10, 8, 7, 10, 4, 9, 10, 8
Video F: Percentiles, Deciles, and Quartiles
1. A person scored at the 92nd percentile on a standardized test. This does not imply that she
earned 92% of the points on the test. State clearly what it means to have a test score at the 92nd
percentile.
2. State the percentile equivalent to the following values:
a) the upper quartile, known as Q3
b) the 4th decile, known as d4
3. The IQR is the Interquartile Range that contains the middle 50% of scores. If the upper quartile
of a set of employee hourly wages was $13.92 and Q1 was $10.88, identify the IQR.
Video G, H, and I: Measures of Spread and Standard deviation and Variance
1. The age in years of four managers randomly selected at a tech company are 28, 31, 33, and 40.
a) Calculate the mean, variance and standard deviation of the ages
b) Explain the meaning of the standard deviation of ages to someone who has never heard of it
before.
2. The standard deviation of a sample of five scores is 0. The max score is 12. What is the mean?
Justify.
Video J: Statistics on the Calculator
1. A freshman in college who conquered AP Statistics in high school is tutoring college Statistics students for $20/hr. The amounts earned weekly for five consecutive weeks in the middle of first semester were $240, $180, $320, $260, and $200. Calculate the mean weekly earnings and the standard deviation of weekly earnings using the calculator.
Videos K, L, and M: Stem Plots and Box Plots
1. Use the following stem plot to answer the questions that follow. The stem plot is for scores earned by players on a video game.
4 7
5 3 6 8
6 0 2 5 7 9
7 1 1 3 4 6 8
8 0 4 6 7
9 3
10 0
11
12
13
14 5
7 1 = 7100 points
a) Determine the five-number summary
b) Are there any outliers? Justify your answer.
c) Sketch a modified box plot of the data.
2. Use the side-by-side box plots of employee wages at two different stores to answer the questions that follow. The top box plot is for wages at Store A. The bottom box plot is for wages at Store B.
$9 10 11 12 13 14 15 16 17 18
Dollars per Hour
a) What percentage of employees earn at least $11 per hour in Store A? Store B?
b) Which store has a higher median? Third Quartile?
c) Identify the IQR of wages at each store? What does this indicate bout the spread of wages?
d) A person earning a median wage at Store A is only at what percentile for Store B?
Videos O, P, Q, and R: Describing and Comparing Distributions and the Mean v Median Implications
1. Use the side-by-side box plots of employee wages at two different stores to answer the questions that follow. The top box plot is for wages at Store A. The bottom box plot is for wages at Store B.
$9 10 11 12 13 14 15 16 17 18
Dollars per Hour
a) Describe the distribution of wages at Store A.
b) The standard deviation of wages at Store B is $1.08. Describe the distribution of wages at
Store B
c) Compare the distribution of wages at Store A to the distribution of wages at Store B.
2. The following statistics are for dollars spent on textbooks and resources for a full-time semester of college classes at Thrifty University. The sample size was 74 students.
Min: $92
LQ: $178
Median: $255
Mean: $291
UQ: $315
Max: $703
Std dev: $184
a) Are there any outliers present?
b) Describe the distribution.
3. The following statistics are for dollars spent on textbooks and resources for a full-time semester of college classes at Billmore University. The sample size was 71 students.
Min: $192
LQ: $297
Median: $396
Mean: $401
UQ: $515
Max: $603
Std dev: $150
a) Compare the distribution of textbook and resource costs at Billmore to the distribution of
textbook and resource costs at Thrifty University featured in problem 2.
b) If a student was randomly selected from a school and spent $472 on textbooks and
resources, which of the two schools are they most likely attending? Why?
Video S and T: Statistics, Parameters, and Unbiased Estimators
1. Identify which numerical values are statistics and which are parameters.
a) In a recent sample of 848 restaurants nation-wide, 17% of them failed a health inspection.
b) The mean score on the final exam in the 3rd period class was 85.7%. All 28 students took the
exam.
c) The mean income of the 48 employees in a company is $64,235.
2. A population is skewed right with a mean of 70 and standard deviation of 5. A simple random sample of 50 is taken from the population.
a) Is the sample mean an unbiased estimator of the population mean? Explain.
b) Is the sample mean an unbiased estimator of the population median? Explain.
c) If the population was normally distributed, would the sample mean be an unbiased estimator
of the population median?
Video U: Transformation of Variables
1. The median and IQR for times to complete a driver’s test were 33 minutes and 11 minutes, respectively. And the standard deviation was 8 minutes. If the times were given in seconds, identify the median of the times and the standard deviation of the times.
2. Test scores have a mean of 77 and a standard deviation of 8 points. If 3 points were added to every test score, identify the new mean and standard deviation.
3. The mean and standard deviation of wages earned this week by a group of computer programmers is $2034 and $390, respectively. The owner decided to give each programmer an 20% increase in pay this week as a bonus. Identify the mean and standard deviation with the bonus included.
Video N: Ogive
1. Below is an ogive of the distribution of hours taken to train employees on a new operating system.
a) Create a box plot of the data
b) Describe the distribution.