CCM IA Unit 2 Warmup

The grades on the last quiz were:

98 100 76 85 95 96 96 81 88 93 92 98 100 73

1. Find the median of the data. 942. How would an additional 85 affect the data?

An 85 would lower the median to 93.

Homework Solutions for U2D4 HW:

Document Camera

MIA U2D5 MEANObjective:

Students will be able to…• Interpret data based on the shape of a data

distribution• Choose the appropriate measures of center

(mean or median) and spread (standard deviation or interquartile range) to describe the distribution.

• Interpret summary statistics for center and spread in the context of the data.

Describing Data Numerically• Measures of Center –

mean, median

• Measures of Spread – range, interquartile range, standard deviation

S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Think About the SituationUse cubes to make stacks representing each household. Use the stacks to answer the following questions.What is the median of these data?

Adapted from Data About Us, Connected Mathematics 2, Grade 6

Ossie

Leon

Gary

Ruth

Paul

Arlene

Finding the Mean

Adapted from Data About Us, Connected Mathematics 2, Grade 6

Ossie

Leon

Gary

Ruth

Paul

Arlene

Make stacks all the same height by moving cubes.

Finding the Mean• How many cubes are in each stack?• By leveling out the stacks to make them equal

height, you have found the average, or mean, number of people in a household. What is the mean number of people per household?

Adapted from Data About Us , Connected Mathematics 2, Grade 6

Ossie

Leon

Gary

Ruth

Paul

Arlene

Investigation 1: Finding the Mean

Student Name

Number of People

in Household

Reggie 6

Tara 4

Brendan 3

Felix 4

Hector 3

Tonisha 4

• How many people are in the six households altogether? Explain.

• What is the mean number of people per household for this group? Explain how you got that number.

• How does the mean for this group compare to the mean of the first group?

• What are some ways to determine the mean number of a set of data other than using cubes? How do these methods relate to the method of using the cubes?

Mean as a Fair Share

• Mary – 7 cookies

• Tom – 6 cookies

• Julio – 2 cookies

Mean as a Fair Share

• How many cookies will each child get if they each get an equal share?

Mean as a Balance Point

2 43 5 6 7

Mean as a Balance Point

Mean as a Balance Point

Mean as a Balance Point

Mean as a Balance Point

Mean as a Balance Point

Mean as a Balance Point

Mean as Balance Point

Mean as a Balance Point

Thinking About the Situation

The Formula

n

xx

x

valuesdata ofnumber

valuesdata of sum

Investigation 2: Data with the Same Mean1) Find two new data sets for six households that each have a mean of 4 people

per household. Use cubes to show each data set. Then make dotplots from the cubes.

2) Find two different data sets for seven households that each has a mean of 4 people per household. Use cubes to show each data set. Then make dotplots from the cubes.

3) A group of seven students find that they have a mean of 3 people per household. Find a data set that fits this description. Then make a dot plot for this data.

4) A group of six students has a mean of 3.5 people per household. Find a data set that fits this description. Then make a dot plot for this data.

5) How can the mean be 3 ½ people when “half” a person does not exist?

6) How can you predict when the mean number of people per household will not be a a whole number?

Investigation 3: Using the Mean

Investigation 3: Using the Mean1) Find the following:

a) the total number of studentsb) the total number of movies watchedc) the mean number of movies watched

2) A new value is added for Carlos, who was home last month with a broken leg. He watched 31 movies.a) How does the new value change the distribution on the

histogram?b) Is this new value an outlier? Explain.c) What is the mean of the data now?d) Compare the mean from question 1 to the new mean.

What do you notice? Explain. e) Does this mean accurately describe the data? Explain.

3) Data for eight more students is added.a) Add these values to the list in your calculator.

How do these values change the distribution on the histogram?

b) Are any of these new values outliers?c) What is the mean of the data now?

5 10 15 20 250

1

2

3

4

5

6

7

8

9

Movies Watched

Number of Movies

Num

ber o

f Stu

dent

s

How do I know which measure of central tendency to use?

http://regentsprep.org/REgents/math/ALGEBRA/AD2/measure.htm

Investigation 4: Mean vs. Median

The heights of Washington High School’s basketball players are: 5 ft 9in, 5 ft 4in, 5 ft 7 in, 5ft 6 in, 5 ft 5 in, 5 ft 3 in, and 5 ft 7 in. A student transfers to Washington High and joins the basketball team. Her height is 6 ft 10in.

Discuss and solve in your groups!

Mean vs. Median

http://www.stat.tamu.edu/~west/ph/meanmedian.html

Mean vs. MedianMound-shaped

and symmetrical (Normal)

Skewed Left

Skewed Right

DISTRIBUTE INTERIMS

Homework

HW1: U2D5 HW

AND GET INTERIMS SIGNED!!!