Samples and Populations: Making Comparisons and Predictions Name: ___________________ Per: _____
Investigation 1: Making Sense of Samples
Date
Learning Target/s
Mon, Apr. 18 Calculate measures of center
and measures of variability.
Classwork
Pg. 2-3: SP 1.1 –
Using Center and
Spread, Part 1

Pg. 4 – SP 1.1,
Part 1
Zaption


Pg. 5-6: SP 1.1 –
Using Center and
Spread, Part 2

Pg. 7 – SP 1.1,
Part 2 Zaption

Pg. 8-9: SP 1.2 –
Using MAD to
Compare
Samples
Pg. 11-12: SP 1.3
– Categorical
Data
Pg. 14-16: SP 1.4
– Using the IQR
to Compare
Samples
Check Up 1

Pg. 10 – SP
1.2 Zaption


Pg. 13 – SP
1.3 Zaption


Vocabulary
Quizizz
Pg. 17 – SP
1.4 Zaption
Pg. 18 – SBAC
Review 4
Zaption



Tues, Apr. 19
Weds,
Apr. 20
Use the MAD to compare
samples.

Thurs,
Apr. 21
Use relative frequencies to
compare samples.

Fri, Apr. 22
Use the interquartile range
Earth Day
(IQR) to compare samples.
Mon, Apr. 25

Tues, Apr. 26

Inv. 1
Self-Assess
Your Learning

Use measures of center and
measures of variability to
compare data sets.
Assess understanding
Investigation 1 learning
targets.
Homework


CCSS.MATH.CONTENT.7.SP.B.3
Informally assess the degree of visual overlap of two numerical data distributions with similar
variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of
variability. For example, the mean height of players on the basketball team is 10 cm greater than the
mean height of players on the soccer team, about twice the variability (mean absolute deviation) on
either team; on a dot plot, the separation between the two distributions of heights is noticeable.
CCSS.MATH.CONTENT.7.SP.B.4
Use measures of center and measures of variability for numerical data from random samples to draw
informal comparative inferences about two populations. For example, decide whether the words in a
chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourthgrade science book.
Parent/Guardian Signature: ________________________________ Due: ____________________
1
SP 1.1, Part 1: Comparing Performances – Using Center and Spread
What is variability?
Measures of Center: Mean and Median
How do you calculate the mean?
How do you calculate the median?
Mean: 5, 8, 10, 12, 7
Median: 5, 8, 10, 12, 7
Mean: 50, 45, 37, 40, 45, 60
Median: 50, 45, 37, 40, 45, 60
A. 1. Find the mean of Jun’s scores (80, 60, 100). Show your calculations.
2. Find the median of Jun’s scores (80, 60, 100). Show how you found it.
3. Find the mean of Mia’s scores (75, 80, 85). Show your calculations.
4. Find the median of Mia’s scores (75, 80, 85). Show how you found it.
5. Use the measures of center you found in parts 1 and 2. Compare Jun’s and Mia’s test performance.
Write at least two complete sentences.
2
Measures of Variability: Range and Mean Absolute Deviation
How do you calculate the range?
How do you calculate the mean absolute deviation (MAD)?
Range: 5, 8, 10, 12, 7
MAD: 5, 8, 10, 12, 7
B. 1. Determine the range of Jun’s test scores (80, 60, 100). Show your calculations.
2. Determine the mean absolute deviation (MAD) of Jun’s test scores (80, 60, 100). Show your
calculations.
3. Determine the range of Mia’s test scores (75, 80, 85). Show your calculations.
4. Determine the MAD of Mia’s test scores (75, 80, 85). Show your calculations.
5. Use the measures of spread you found in parts 1 and 2. Compare Jun’s and Mia’s test performances.
Write at least two complete sentences.
3
Homework: SP 1.1, Part 1 – Complete and correct with Zaption
Diver
Jarrod
Pascal
Dive 1
8.5
9.3
Dive 2
8.1
7.5
Dive 3
6.4
8
Dive 4
9.5
8.5
Dive 5
10
9.2
1. Find the measures of center for the two divers.
Student Median
Mean
Jarrod
Pascal
2. Compare the measures of center for the two divers. Write at least two complete sentences.
3. Find the measures of variability for the two divers.
Student Range
MAD
Jarrod
Pascal
4. Compare the measures of variability for the two divers. Write at least two complete sentences.
4
SP 1.1, Part 2: Comparing Performances – Using Center and Spread
C. Think about when you looked at Jun and Mia’s test scores from the first quarter (on pages 2 and 3) and
analyzed the measures of center and variability. Do you have enough data to make any general statements
about Jun’s or Mia’s overall math test performance? Explain. Write at least two complete sentences.
D. Jun’s score mid-year: 80, 60, 100, 80, 80, 80
Mia’s scores mid-year: 75, 80, 85, 80, 80, 100
1. Find the median of Jun’s data (80, 60, 100, 80, 80, 80). Show how you found it.
2. Find the median of Mia’s data (75, 80, 85, 80, 80, 100). Show how you found it.
3. Find the mean of Jun’s data(80, 60, 100, 80, 80, 80). Show your calculations.
4. Find the mean of Mia’s data (75, 80, 85, 80, 80, 100). Show your calculations.
5. Use each measure of center (median and mean) to compare Jun’s scores and Mia’s scores. Write at
least two complete sentences.
5
6. Find the range of Jun’s data (80, 60, 100, 80, 80, 80). Show your calculations.
7. Find the range of Mia’s data (75, 80, 85, 80, 80, 100). Show your calculations.
8. Find the MAD of Jun’s data (80, 60, 100, 80, 80, 80). Show your calculations.
9. Find the MAD of Mia’s data (75, 80, 85, 80, 80, 100). Show your calculations.
10. Use each measure of variability (range and MAD) to compare Jun’s scores and Mia’s scores. Write at
least two complete sentences.
6
Homework: SP 1.1, Part 2 – Complete and correct with Zaption
1. What are the measures of center? What do they tell us about a data set?
2. What are the measures of variability? What do they tell us about a data set?
3. Summarize the statistics you found in class today (see pages 5 and 6):
Student Median
Mean
Range
Jun
MAD
Mia
4. Decide whether you agree or disagree with each statement below. Use the statistics you found in the
earlier questions. Explain your reasoning. Write at least two complete sentences for each statement.
a. One student is a stronger math student than the other.
b. One student is more consistent than the other.
c. The two students perform equally well on math tests.
d. You can make better comparisons using the larger data set.
7
SP 1.2: Using MAD to
Compare Samples
Which team is the most
successful and deserves to win
the prize?
A. Make a line plot of
each team’s data. Find
the total money
raised, mean, and
MAD of each data set.
Team
Line Plot
Total $
Raised
Mean
(Add ∆)
MAD
(Add Lines)
1
2
3
4
5
6
8
B. The Hiking Club’s organizers must decide which team is awarded the prize. Each organizer has a different
strategy for determining the most successful fundraising team. For each strategy below, explain whether or
not the strategy helps determine the most successful team. If the strategy helps determine the most
successful team, determine who will win the prize.
1. Bianca: For each team, just add up all the money raised by its members. Then compare to the team
totals.
2. Gianna: Find the mean number of dollars raised by each team. Then compare the team averages.
3. Jonah: Compare the money raised by each member to the team’s average. On average, how far does
each member’s amount differ from the team’s mean amount? For each team, find the MAD. Then
compare the MADs of the six teams.
C. In Question A, you made line plots of the six sets of data. In Question B, you found the MAD of each
distribution. The dot plot shows Team 1’s fundraising amounts. The lines indicate the distances of one
MAD and two MADs from the mean on either side. Count the data points located closer than, but not
including, the distance of one MAD from the mean. The ∆ indicates the mean, 35.
1. How many of Team 1’s data values are
located within one MAD (both less than
and greater than the mean)? Write this
number as a percent.
2. How many of Team 1’s data values are located within two MADs (both less than and greater than the
mean)? Write this number as a percent.
3. How many of Team 1’s data values are more than two MADs away from the mean? Write this number
as a percent.
9
Homework: SP 1.2 – Complete and correct with Zaption
Complete the table. For each team:
a. On the line plot, mark the mean with a triangle, and then mark the location of one and two MADs from
the mean with lines (the mean and MAD of each team are included in the table already).
b. Find the percent of values within one MAD of the mean, two MADs of the mean, and greater than two
MADs from the mean.
Team
Line Plot
Mean
MAD
Percent of Data Within…
1 MAD
2 MADs >2
MADs
1
2
3
4
5
6
10
SP 1.3: Distinguishing Categorical Data from Numerical Data
Categorical Data
Numerical Data
The sample sizes of Internet respondents and 7th graders are different. You can use relative frequencies –
frequencies based on percentages – to compare samples of different sizes.
How do you find relative frequencies?
Ex: What is the frequency of people who prefer to sit on the front of the roller coaster in each sample?
Roller Coaster Seating Preferences
Preference
Front
Votes from
Internet
97
Relative
Frequency
Votes from
7th Graders
27
Middle
50
22
Back
18
14
Total Votes
165
63
Relative
Frequency
Votes From
Our Class
Relative
Frequency
Relative
Frequency
Votes From
Our Class
Relative
Frequency
Other Roller Coaster Preferences
Preference
Airtime
Votes from
Internet
88
Relative
Frequency
Votes from
7th Graders
31
Height
36
24
Inversions
59
29
Smoothness
39
12
Speed
105
57
Total Votes
327
153
11
B. For each survey question, make bar graphs of the three data sets.
Where do you like to sit on a roller coaster?
Internet
7th Graders
Our Class
Which of the following roller coaster characteristics do you prefer? You may choose more than one.
Internet
7th Graders
Our Class
C. Which measure/s of center – mean, median, or mode – can you use to describe these results?
D. For each survey question, write two statements comparing results from the three data sets. Use complete
sentences.
12
Homework: SP 1.3 – Complete and correct with Zaption
This homework assignment is related to our classwork today. Look back at pages 11 and 12 to help you.
1. Write two statements to summarize the data collected from the Roller Coaster Survey. Use complete
sentences.
2. How are the summaries useful?
3. Suppose 400 people ride a roller coaster in one day. How many of them would you predict want to sit at
the front? Explain.
4. The following question was asked in a survey: What is your favorite amusement park ride – roller coaster,
log ride, ferris wheel, or bumper cars? The table below shows the results from an internet survey and from
7th grade students at East Jr. High and West Jr. High.
Favorite Votes from
Relative
Votes from
Relative
Votes from
Relative
Ride
Internet
Frequency
East Jr. High
Frequency
West Jr. High Frequency
Roller
92
42
36
Coaster
Log Ride
26
31
14
Ferris
Wheel
Bumper
Cars
Total
Votes
22
3
6
20
4
4
160
80
60
a. Find the relative frequencies of the data and them to the table.
b. Write three or more statements comparing the data sets. Use complete sentences.
13
SP 1.4: Using the IQR to Compare Samples
A. How might you decide which are faster, steel-frame roller coasters or wood-frame roller coasters? Explain.
22, 22, 35, 35, 35, 35, 40, 42, 45, 45, 48, 48, 50, 50, 54, 55, 55, 60, 61, 63, 66, 66, 70, 70, 73, 75, 76, 80, 85, 90
MEASURES OF CENTER:
Mean: ____
Lower Quartile (LQ): ____
MEASURES OF VARIABILITY:
IQR: ____
Mode/s: ____
Median: ____
Upper Quartile (UQ): ____
Minimum: ____
Maximum: ____
Range: ____
Outlier/s: ____
Steel-Frame Rollercoasters
Box and Whisker Plot:
Line Plot:
14
25, 32, 35, 44, 45, 45, 47, 50, 50, 50, 50, 51, 51, 51, 51, 55, 55, 55, 56, 56, 60, 60, 60, 62, 62, 62, 62, 65, 65, 66
MEASURES OF CENTER:
Mean: ____
Lower Quartile (LQ): ____
MEASURES OF VARIABILITY:
IQR: ____
Mode/s: ____
Median: ____
Upper Quartile (UQ): ____
Minimum: ____
Maximum: ____
Range: ____
Outlier/s: ____
Wood-Frame Rollercoasters
Box and Whisker Plot:
Line Plot:
B. Are steel-frame coasters faster than wood-frame coasters? Explain your reasoning based on statistics. Use
at least three complete sentences.
15
C. Charlie and Rosa wrote the reports below. They used the two distributions of data to compare steel-frame
roller coasters and wood-frame roller coasters. Do you agree with Charlie or with Rosa? Explain your
reasoning. Use at least three
complete sentences.
Extra Challenge: Calculate the MAD for the roller coaster data sets. 
16
Homework: SP 1.4 – Complete and correct with Zaption
1. Use the dot plots below to answer the questions for each distribution.
a. Draw lines on the dot plots to show one and two MADS away from the mean.
b. How many roller coasters have speeds within one MAD of the mean (both less than and greater
than)? Write this number as a percent.
Steel-Frame: __________
Wood-Frame: ____________
c. How many roller coasters have speeds within two MADs of the mean (both less than and greater
than)? Write this number as a percent.
Steel-Frame: __________
Wood-Frame: ____________
d. How many roller coasters have speeds more than two MADs away from the mean? Write this
number as a percent.
Steel-Frame: __________
Wood-Frame: ____________
e. Based on the statistics, which roller coasters go faster? Explain your reasoning.
17
SBAC Practice Test – Part 4
Score: ___ / 3
(Complete and correct with Zaption)
?
Question and Answer
1
A representative sample of 50 students from a high school is surveyed. Each student is asked
what science course he or she is taking. Choose True or False to indicate whether each
statement is valid based on the survey results.
2
The spinner has 8 equal-sized
sections each labled 1, 2,3, or 4.
The arrow on the spinner is spun.
Match the outcomes (landing on
a 1, 2, 3, 4) to the category that
correctly describes the probability
of the outcome.
3
Consider the equation.
Correct
Answer
Identify two expressions that are
equivalent to w in the shaded section.
18