Using the Median as a Measure of Center

Lesson 2

1

Warm Up

OBJECTIVE: SWBAT recognize how the median reacts to changes made to a data set.Language Objective: SWBAT write about what happens to the median when a data set changes.

Agenda

2

3) Do you exercise?

2) How tall are the students in my class?

Determine whether the following questions are statistical or not. Explain how you know.

1) How old am I?

Statistical Question: A question that will have several answers that might be differentScaffolding

A = Not statistical

A = Statistical

A = Not statistical

Launch (A) – Review of Last Class

3

OK, we have learned how to form a statistical question. Now what?!

But then what do we do with the data we collect?

Then what?

Ask a question and collect data!

Organize it!

Examine/analyze the data!

Agenda

Launch (A) Turn and Talk (30 sec)

number of toppings students like on their pizzas

4

When we analyze data, what are we looking for?

Center

Spread

Shape

Median

Mean

Agenda

Today!

Launch (A)

5

What is the definition of median?

The median is the number that marks the middle of an ordered set of data. Half of the values lie at or below the median and half of the values lie at or above the median.

Vocabulary

4 6 6 8 9 10 13

median

Agenda

Launch (A)

6

How do you find the median when there is an even number of data points?

4 6 6 8 10 10 13 14

Agenda

hmmm I have two data points left, 8 and 10…what do I do?

9 = median

Launch (B) – Class Challenge! Whole Class

7

1) On the index card in front of you, write the number of letters in your FIRST name.

2) Stand up with your index card in your hand.

3) Without talking, organize yourselves in a line from least to greatest.

Agenda

Launch (B) Whole Class

8

1) How could we find the median number of letters in students’ names in our class?

3) What would happen if we added another student’s name length to our data?

4) What would happen if that student’s name had 54 letters?

Agenda

2) What is the median number of letters in students’ names?

Explore (A) Individual (Notes)

9

The students in Ms. Jee’s class collected data to answer the statistical question, “How many letters are in the first names of Ms. Jee’s students?” The data is displayed below.

What is the median for these data?

8 34 5

67 6

5

710

3

Agenda

Explore (A) Solution

10

What is the median for these data?

Agenda

median8 3

46

5

7 6

5

710

3

Explore (A)

11

The median of the data is 6 letters.

5 83 4 5 6 77 103

Agenda

6

median

Now that we know the median name length in Ms. Jee’s class is 6 letters, we are going to see what happens to the median when we make changes to the data set.

Explore (A) Think-Pair-Share (Notes)

12

The students in Ms. Jee’s class collected data to answer the statistical question, “How many letters are in the first names of Ms. Jee’s students?” The data is displayed below.

Remove two data points from the original data set so that the median decreases.

5 83 4 5 6 77 103 6

Scaffolding Agenda

Explore (A) Possible Solution

13

Remove two data points from the original data set so that the median decreases.

5 83 4 5 6 76 7 103

83 4 6 7 103 5

Agenda

5

Explore (A) – Class Challenge #2 Think-Pair-Share (Notes)

14

The students in Ms. Jee’s class collected data to answer the statistical question, “How many letters are in the first names of Ms. Jee’s students?” The data is displayed below.

Add two data points to the original data set so that the median stays the same.

5 83 4 5 6 77 103 6

Scaffolding Agenda

Explore (A) Possible Solution

15

Add two data points to the original data set so that the median stays the same.

5 83 4 5 6 76 7 1033 33

Agenda

median

Woah! 33 is far away from the rest of the data! Is there a word for a piece of data that is much smaller or much larger than the rest of the data?

OUTLIER!

Explore (A) Individual

16

Mr. Nunez drives a bus. The line plot below shows the number of passengers that were on his bus for each of the last 10 trips he made.

A = 6 passengers

Agenda

Bus Trips

What is the median for these data? Be prepared to share your strategy.

Explore (A) Turn-and-Talk (30 secs)

17

Mr. Nunez drives a bus. The line plot below shows the number of passengers that were on his bus for each of the last 10 trips he made.

There are 72 passengers on the bus for Mr. Nunez’s 11th trip. How does the median of the original data set change?

Agenda

Bus TripsA = The median

does not change! The median number of passengers remains at 6.

Explore (B)

18

Part 1 - (10 Min)

Work independently and check in with a partner to complete your class work.

1-Worksheet2-Share Out

In 10 minutes you will be asked to stop and share your answers!

Click on the timer!

Agenda

Summary – Student Share Out

19

Part 2 – (10 Min)

Students share out work.

Classwork Questions

Agenda