Answer Key
Population, Parameter, Statistic, Sample
A parameter is a numerical summary of the Population
A statistic is a numerical summary of the Sample
Describing Data
What does the 5 – number summary include?
Minimum, Q1, Median, Q3, Maximum
What are the 2 summary statistics?
Mean(average) and Standard Deviation
Which of the two is influenced by outliers? (circle one) Median
Mean
You can describe shape as
Unimodal, Bimodal, Uniform, Symmetric, skewed right, skewed left, etc.
Categorical or Quantitative Variables
Categorical Variable: Any variable that is a word, or numeric values that can put something into a
category
Quantitative Variable: Numerical values that fall in to a range.
Which of the 5 visuals can be utilized for Categorical Variables?
Pie Chart
Bar Graph
Pareto Chart
Which of the 5 visuals can be utilized for Quantitative Variables?
Histogram
Box Plot
Answer Key
Visuals
What is the difference between a Pareto Chart and a Bar Chart? ___________________________
Match each graph with its Name
Pareto Chart
Bar Graph
Pie chart
Box plot
Histogram
Label each graph with the type of distribution it has
Skewed Right
Bimodal
Symmetric/ normal
Normal Distribution
What is the shape of a normal distribution? Symmetric, Unimodal, Bell-shaped
What does the empirical rule state? 68-95-99.7% Rule
68% of the data falls within 1 standard deviation of the mean
95% of the data falls within 2 standard deviation of the mean
99.7% of the data falls within 3 standard deviation of the mean
*What does a z-score tell you? How many standard deviations away from the mean.
Skewed Left
Answer Key
Population, Parameter, Statistic, Sample
 You are looking at the average age of all American alligators, you select 15 alligators off the
coast of Florida and track them to see how old they become. The average of these 15 live to be
12. The true average age alligators live to is 16.
Population: All American Alligators
Parameter: 16 years old
Sample: the 15 alligators
Statistic: 12 years old
 Your dog can jump 2.5 feet. This leads you to believe your dog can jump farther than any other
dog. However, the American record book has a dog that can jump 6.48 feet.
Population: American dogs
Parameter: 6.48 feet
Sample: My dog
Statistic: 2.5 feet
The Iowa state football team has an average height of 6’2”. The NCAA average height for football
players is 6’. You then conclude the ISU team is pretty tall.
Population: NCAA football players
Parameter: 6’
Sample: ISU football players
Statistic: 6’2”
 Oak trees live to be an average age of 263 years. The oak trees in America have been known to
live an average of only 123 years.
Population: All oak trees
Parameter: 263 years
Sample: American oak trees
Statistic: 123 years
Answer Key
Categorical or Quantitative
C Top 10 websites
C Number of roll – over car accidents based on car brand
C The baggage fees for different airlines collected each year
Q Price of cars people purchased in 2008
C Regional rain fall
C sales for 4 types of smart phones
Q Height of 200 random people in Iowa
Q Net Income
C Wine exports of the top 5 wine-exporting countries
Visuals
Draw a Boxplot (2,3,4,5,6,7,8,8,8,8,9,9,10)
1
2
3
4
5
6
7
8
9
10
9
10
Draw a Histogram (same numbers as above)
8
6
4
2
1
2
3
4
5
6
7
8
Answer Key
Draw a Bar Chart – car sales
180,000
150,000
120,000
90,000
60,000
30,000
Chrysler
2
Ford
GM
Honda Nissan Toyota
Normal
Using z-scores
a) P (Z < 1.5)
d) P (|Z| < 1.2)
0.9332
0.7698
b) P(Z < z) = 0.35
e) P(Z > z) = 0.60
Z=-0.38
c) P (Z > - 1)
0.8413
-0.25
f)
P (Z > 0.5)
0.3085
The times for the 100m freestyle for the womens swim team is evenly distributed with a
mean of 59.6 sec. and a standard deviation of 1.2 seconds.
Concepts
a)
What time can 50% of the teammates complete a 100m freestyle in?
59.6 seconds
b)
What percent of swimmers can complete a 100m freestyle between 58.4 seconds and 60.8 seconds.
68%
c)
Jane brags that she can swim the race faster than 97.5% of her teammates? What would her time be?
57.2 seconds
d)
If Jenny is wanting to make the team and she can swim a 100 m freestyle in 61 seconds, do you think she would make
the team?
Probably not because at least 84% of the team can swim faster than her.
Orrrr yes because there is still at least 2.5% of the team that is slower than her.
e)
What is the probability that one of the girls will beat the opponents fastest swimmer that can swim a 100 m freestyle
in 56 seconds?
0.15%
Opening weekend, Marvel films gross sales are normally distributed making an average of
$68,326,910 and a standard deviation of $22,442,000.
a)
X-men only made $55,101,604, how many standard deviations does this movie fall from the mean.
𝑧=
𝑥−𝜇
𝜎
𝑧=
55101604−68326910
22442000
= -0.59.
X-men falls 0.589 standard deviations to the left of the mean.
Concepts
b)
Thor: The Dark World had an opening box office sales of $85,737,841. What percentile does Thor2 fall under
𝑧=
𝑥−𝜇
𝜎
𝑧=
85737841−68326910
22442000
= 0.78
Thor: The Dark World is in the 78th percentile for opening weekend sales.
c)
The Avengers made $207,438,708. What percentile does this fall under
𝑧=
𝑥−𝜇
𝜎
𝑧=
207438708−68326910
22442000
= 6.2
The Avengers is in greater than the 99.98th percentile for opening weekend sales.
d)
If the new spiderman is hoping to hit at least the 40th percentile, how much money is it expecting to make opening
weekend in gross sales?
𝑧=
𝑥−𝜇
𝜎
−0.25 =
𝑥−68326910
22442000
=> x= $62,716,410
The new spiderman is hoping to make at least $62,716,410 their opening weekend.