Unit 10: Statistics

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Transcript Unit 10: Statistics

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.
94
2. 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 MEAN
Objective:
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 Situation
Use cubes to make stacks representing each
household. Use the stacks to answer the
following questions.
What is the median of these data?
Ossie
Paul
Gary
Leon
Ruth
Arlene
Adapted from Data About Us, Connected Mathematics 2, Grade 6
Finding the Mean
Make stacks all the same height by moving
cubes.
Ossie
Paul
Gary
Leon
Ruth
Arlene
Adapted from Data About Us, Connected Mathematics 2, Grade 6
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?
Ossie
Gary
Leon
Paul
Ruth
Arlene
Adapted from Data About Us , Connected Mathematics 2, Grade 6
Investigation 1: Finding the Mean
Number of
Student Name
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
3
4
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
sum of data values
x
number of data values
x

x
n
Investigation 2: Data with the Same Mean
1) 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 Mean
1) Find the following:
a) the total number of students
b) the total number of movies watched
c) 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?
Movies Watched
9
8
Number of Students
7
6
5
4
3
2
1
0
5
10
15
Number of Movies
20
25
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. Median
Mound-shaped
and symmetrical
(Normal)
Skewed
Left
Skewed
Right
DISTRIBUTE INTERIMS
Homework
HW1: U2D5 HW
AND GET INTERIMS SIGNED!!!