Data About us

Name: ___________________ Per: _____

Investigation 3-4: MAD and Measures of Variability Date

Learning Target/s

Classwork

Thurs., June 8

Understand the MAD is measure of variability

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Pg. 2-4: DAU 3.3: Introduction to MAD

Fri., June 9

Calculate the MAD and draw conclusions

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Pg. 2-4: DAU 3.3 continues

Mon., June 12

Students can calculate the MAD score of any set of DATA

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Pg. 6DAU- MAD activity

Homework 

Pg. 5 – Correct online

Self-Assess Your Learning

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Pg. 7: DAU INV. 3-4 review Correct online

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Upcoming Assessments:  June_____________________________– Data About Us Test 6th Grade Common Core State Standards 6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers 6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape . 6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.B.5a Summarize numerical data sets in relation to their context, such as by reporting the number of observations. 6.SP.B.5c Summarize numerical data sets in relation to their context, such as by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 6.SP.B.5d Summarize numerical data sets in relation to their context, such as by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. 6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.C.7 Understand ordering and absolute value of rational numbers.

I have reviewed this packet and I am satisfied with the work completed:

Due: ________________

Student Signature: _______________________________ Parent/Guardian Signature: ________________________

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3.3 Determining and Describing Variability Using that MAD In your lifetime you spend a lot of time waiting. Sometimes it feels like you stand in line forever. For example, you may wait a long time for your favorite ride at an amusement park. During the summer, one estimate of average wait time at an amusement park is 60 minutes. The most popular rides can accommodate 1,500 people per hour. Lines form when more people arrive than rides fit. Amusement parks are designed to minimize wait times, but variability in the number of people who choose a particular ride can result in lines. Sally and her family spend the day at an amusement park. At the end of the day, Sally noticed the sign.

i.

Sally waits in line LONGER than 25 minutes for the Scenic Trolley ride. How could this have happened?

A. Since Sally waited in line longer than the average wait time, she wondered how much wait times vary. The dot plot below shows a distribution of 10 wait times for the Scenic Trolley ride.

1. Sally says that the mean wait time is 25 minutes, just like the sign claimed. Do you agree? Show how you know.

2. Sally wonders how typical a wait time of 25 minutes is. She says “I can find how much, on average, the data varies from the mean time of 25 minutes.” She uses the graph below to find the distance each data value is from the mean. 2

Fred Says “That’s a good idea, but I used an ordered-value bar graph to show the same idea.”

3. Describe how you can use each graph to find how much, on average, the data values vary from the mean time of 25 minutes.

4. What does this information tell you about how long you might have to wait in line to ride the Scenic Trolley?

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Sally and Fred calculated a statistic called the mean absolute deviation (MAD) of the distribution. It is the average distance (or mean distance) from the mean of all data values. B. Below is a sample of 10 wait times for the Carousel, which also has a mean wait time of 25 minutes (indicated by the triangle)

1) Find the mean absolute deviation (MAD) for this distribution.

2) Compare the MAD for the Scenic Trolley with the MAD for the Carousel. Explain why might you choose the Carousel over the Scenic Trolley?

C. The Bumper Cars have a mean wait time of 10 minutes. Like other rides, the wait times are variable. Below is a sample of 10 wait times for the bumper cars.

3) Find the mean absolute deviation (MAD) for this distribution.

4) Compare the mean wait time of the Scenic Trolley and of the Bumper Cars. What do you notice? Then compare the MADS of both rides. Explain what you notice?

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3.3 Homework: Determining and Describing Variability Using that MAD The dot plots below show the distributions of 10 waits at 2 rides.

Amusement Park Ride 1

Amusement Park Ride 2

Mean

MAD

Compare the MAD’s. In which distribution do the data vary more from the mean?

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MAD: Extra Practice

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Investigation 3-4 Review: Name (Soda) Caffeine in 8 oz (mg)

A 38

B 37

C 27

D 27

E 26

F 24

G 21

H 15

I 23

Calculate each: Mean

Median Mode Max MIN. Range UQ LQ Interquartile Range Score (IQR) MAD

Plot the Box and Whisker Plot:

A. What three measures would you use to describe the variability of a set of data? 1. 2. 3. B. What two measures would you use to describe the measures of center? 1. 2. 7