U8L10 Finding and Interpreting Mean

Which One Doesn’t Belong:
Division

Warm Up 10.1

Open Ended

Which expression does not belong? Be prepared to explain your reasoning.

$$\frac{8+8+4+4}{4}$$ $$\frac{10+10+4}{4}$$ $$\frac{9+9+5+5}{4}$$ $$\frac{6+6+6+6+6}{5}$$

Finding and Interpreting the
Mean as the Balance Point

Lesson # 10

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2019 Open Up Resources |

Let’s look at another
way to understand
the mean of a data
set.

Today’s Goals

❏ I can describe what the mean tells us in the context of the

data.

❏ I can explain how the mean represents a balance point for

the data on a dot plot.

Travel Times: Part 1

Activity
●MLR 1: Stronger & Clearer Each Time

Draw

Here is the data set from an earlier lesson showing how long it takes for Diego to walk to school, in minutes, over 5 days. The mean number of minutes was 11.

Represent Diego’s data on a dot plot. Mark the location of the mean with a triangle ( $$\Delta$$ ).

Draw

The mean can also be seen a measure of center that balances the points in a data set. If we find the distance between every point and the mean, add the distances on each side of the mean, and compare the two sums, we can see this balancing.

Open Ended

What do you notice about the two sums?

Work with a partner to answer the first two questions ( 5 min)

3. Can another point that is not the mean produce
similar sums of distances?
Letʼs investigate whether 10 can produce similar
sums as those of 11.

a.Complete the table with the distance of each
data point from 10.

b.Sum of distances left of 10:___________ Sum of
distances right of 10:___________
What do you notice about the two sums?

4. Based on your work so far, explain why the mean
can be considered a balance point for the data set.

Let’s Talk About It!

●

How are the sums of distances to mean (11 minutes) and the sums of
distances to another point other than the mean (e.g., 10 minutes)
different?

●

If you choose another point or location on the number line, would it
produce equal sums of distances to the left and to the right?

Travel Times (Part 2)

Activity 10.3
●MLR5: Co-Craft Questions & Problems

● Work Quietly ( 5 min)
● Discuss with your partner (2-3 min)

Here are dot plots showing how long Diegoʼs trips to school took in minutes—which you studied
earlier—and how long Andreʼs trips to school took in minutes. The dot plots include the means for each
data set, marked by triangles.

a.Which of the two data sets has a larger mean? In this context, what does a larger mean tell us?

b.Which of the two data sets has larger sums of distances to the left and right of the mean? What do
these sums tell us about the variability in Diegoʼs and Andreʼs travel times?

Work with your partner (5 min)

Here is a dot plot showing lengths of Linʼs trips to
school.

a.Calculate the mean of Linʼs travel times.

b.Complete the table with the distance between
each point and the mean as well as whether the
point is to the left or right of the mean.

c.Find the sum of distances to the left of the
mean and the sum of distances to the right of
the mean.

d.

Use your work to compare Linʼs travel times to
Andreʼs. What can you say about their average
travel times? What about the variability in their
travel times?

Let’s Talk About It

●

How do the data points in Linʼs dot plot compare to those in Andreʼs?

●

How do their means compare? How do their sums of distances from the
mean compare?

●

What do the sums of distances tell us about the travel times?

●

If more than half of Linʼs data points are far from the mean of 14 minutes, is
the mean still a good description of her typical travel time? Why or why
not?

Measure of

Center

A measure of center is a value that
seems typical for a data distribution.

Mean and median are both
measures of center.

Lesson Synthesis

In this lesson, we learn that the mean can be interpreted as the balance point of a
distribution.

●How does the mean balance the distribution of a data set?

●How can a dot plot help us make sense of this interpretation?

●Could another value—besides the mean—balance a data distribution? How
can we tell?

Lesson Synthesis

We also learn that the mean is used as a measure of center of a distribution, or a
number that summarizes the center of a distribution.

●
Why might it make sense for the mean to be a number that describes the
center of a distribution?

●
In earlier lessons, we had used an estimate of the center of a distribution to
describe what is typical or characteristic of a group. Why might it make sense
to use the mean to describe a typical feature of a group?

●
●

Today’s Goals

❏ I can describe what the mean tells us in the context of the

data.

❏ I can explain how the mean represents a balance point for

the data on a dot plot.

Text Messages

Cool Down 10.4

The three data sets show the number of text messages sent by Jada, Diego, and Lin
over 6 days. One of the data sets has a mean of 4, one has a mean of 5, and one has a
mean of 6.

1.Which data set has which mean? What does this tell you about the text messages
sent by the three students?

2.

Which data set has the greatest variability? Explain your reasoning.