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Teacher Copy
Activity 28
Measures of Center
Bull's Eye
Lesson 28-1
Mean and Outliers
Learning Targets
Calculate the mean of a data set.
Identify outliers of a data set.
Construct dot plots.
KWL Chart (Know, Want to Know, Learn) (Learning Strategy)
Definition
Activating prior knowledge by identifying what students know, determining what they want to
learn, and having them reflect on what they learned
Purpose
Assists in organizing information and reflecting on learning to build content knowledge and
increase comprehension
Vocabulary Organizer (Learning Strategy)
Definition
Using a graphic organizer to keep an ongoing record of vocabulary words with definitions,
pictures, notes, and connections between words
Purpose
Supports a systematic process of learning vocabulary
Marking the Text (Learning Strategy)
Definition
Highlighting, underlining, and /or annotating text to focus on key information to help understand
the text or solve the problem
Purpose
Helps the reader identify important information in the text and make notes about the
interpretation of tasks required and concepts to apply to reach a solution
p. 363
Think-Pair-Share (Learning Strategy)
Definition
Thinking through a problem alone, pairing with a partner to share ideas, and concluding by
sharing results with the class
Purpose
Enables the development of initial ideas that are then tested with a partner in preparation for
revising ideas and sharing them with a larger group
Suggested Learning Strategies
KWL Chart, Vocabulary Organizer, Marking the Text, Think-Pair-Share
The distribution of numerical data can be described by discussing its center, spread, p. 366p. 365p. 364
and shape. In this activity, you will investigate the center of distributions.
Look at the following heights (in inches) of students on the soccer team.
57 55 60 55 56 60 56 62 57 55 61 54
57 53 58 58 54 56 59 57 61 60 59
Here is the dot plot for this data.
1. Estimate the center of the distribution for height of students on the soccer team from the
information contained in the dot plot.
2. Calculate the mean height of students in your class. (Round your answer to the nearest
tenth of an inch.)
Math Tip
To calculate the mean (or average) of the values in a distribution, compute the total of the
data values by adding all of the values. Then divide this total by the number of observations.
3. How close was your estimate to the actual mean height of students? Explain why your
estimate is or is not close to the actual mean. Share your response with your group. As
you explain your reasoning, speak clearly and use precise mathematical language.
Look at data on the amount of time that several students spent taking a history test. Below is the
data set, along with a dot plot of that data.
40 30 23 35 28 29 15 37 38 38 36 35
35 32 34 39 36 37 32 35 34 34 36 35
4. Estimate the mean length of time to finish the test for these students by looking at the dot
plot.
5. Calculate the mean length of time for these students to finish the test. (Round your
answer to the nearest tenth of a minute.)
6. How close was your estimate to the actual mean length of time? Explain why your
estimate was (or was not) close to the actual mean.
In this data set, the observations of 15 minutes and 23 minutes appear to be unusual values.
Values that are outside the general pattern of data are called outliers.
Math Terms
Outliers are observations that do not fit the overall pattern of the data set.
7. Reason abstractly. What is a possible reason why someone might finish this test so
quickly?
Sometimes unusual values like these are correct data values. For example, in the case of height, a
data value may look unusual because a student may have reported height in feet rather than in
inches. In other cases, these unusual values represent errors—data that was recorded incorrectly
or false answers that someone gave to a survey. (For example, suppose a student recorded height
as 100 feet or the time to take a test as −4 minutes. These data values would be considered
incorrect.)
If an outlier is thought to be an incorrect data value, then it is removed from the data set.
However, if an outlier might be a correct data value, it is NOT removed from the data set,
although it might need to be corrected. For example, if it were clear that height had been reported
in feet rather than in inches, you would convert the measurement to inches and keep it in the data
set.
8. Should the observation of 15 minutes or 23 minutes be removed from the data set above?
Explain why or why not.
9. Predict what would happen to the mean if these two observations, 15 minutes and 23
minutes, were removed.
10. Remove these two observations and calculate the mean length of time to finish the test
for the remaining 22 times.
11. Was your prediction in Item 9 correct? If not, explain why not.
12. State in words what effect these two unusual observations had on the mean length of
time to finish the test.
A women's swim team includes ten members who swim relays. Their ages are listed below.
21 19 22 21 22 18 22 20 41 24
13. Create a dot plot of the ages of these relay swimmers.
14. Calculate the mean age for the relay swimmers.
15. Enter each of the 10 ages into the appropriate column in the table below, depending on
whether it is above or below the mean age. For example, 21 is below the mean age, so it
would be entered into the first column. Once you have entered the 10 ages, complete the
rest of the table.
Data Values Below
the Mean
Distance from
Mean
Data Values Above
the Mean
Distance From
Mean
Total distance:
Total distance:
16. What do you notice about the total distance from the mean for the values below the mean
versus the total distance from the mean for the values above the mean?
17. Do you think this is true for any data set?
18. Is there an outlier in this age distribution? If so, what would be the mean if this value were
removed?
Check Your Understanding
19. Explain how to calculate the mean of a data set.
20. What is an outlier?
21. Summarize the effect of outliers on the mean of a distribution.
Lesson 28-1 Practice
22. Alex works in a grocery store after school. Here is his list of hours for a two-week period:
4 3 3 4 4 4 8 3 4 3
a. Are there any outliers? If so, what are they?
b. Is the outlier a correct data value?
c. What might explain the outlier?
23. Calculate the mean.
24. Construct viable arguments. Describe the effect of the outlier on the mean.
25. Construct a dot plot representing the hours Alex worked.
26. In a few sentences, describe what the dot plot shows.
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