Download Warm-Up

Lesson 4.6
Core Focus on
Ratios, Rates & Statistics
Analyzing Statistics
Warm-Up
For each data set find the five-number summary and
create a box-and-whisker plot.
1. 1, 4, 4, 7, 9, 10, 11, 17, 22
1 ~ 4 ~ 9 ~ 14 ~ 22
2. 49, 54, 56, 42, 51, 58, 53
42 ~ 49 ~ 53 ~ 56 ~ 58
Lesson 4.6
Analyzing Statistics
Analyze how characteristics of a data set
affect the measures of center.
Explore!
What’s the “Mean”ing?
Mr. Hinton was curious about the average number of letters in each of his
students’ names. The names of eight of his students are listed below.
Paul, Rob, Ana, Javon, Savannah, Ali, Juan, Alexandria
Step 1 Find the number of letters in each of the eight names.
Step 2 For each student, make a stack of cubes with the height matching the number
of letters in their name. For example, Paul’s stack should be 4 cubes tall.
Step 3 Look at the stacks. What is the mode?
Step 4 Put the stacks in order from shortest to tallest. Find the median.
Step 5 Without adding any more cubes, “level” the stacks by redistributing blocks so
that all eight stacks have the same height. How many cubes are in each stack?
Step 6 If each of Mr. Hinton’s eight students had the same number of letters in their
name, how many letters would each person have? Which measure of center
does this value represent?
Step 7 Which measure of center best represents the data? Explain your reasoning.
Explore!
What’s the “Mean”ing?
Step 8 Copy the dot plot below onto a sheet of paper. The numbers (instead of dots)
on the top of the dot plot represent how far each value is away from the mean.
These numbers are called absolute deviations from the mean. For example,
Paul is represented by a “1” since his name has 4 letters – 1 away from the
mean of 5. Rob and Ana are each represented by a “2” since they are 2 away
from the mean. Which student does the “3” represent?
Each absolute deviation
from the mean is
written as a positive
number.
Step 9 The dot plot is missing numbers representing Ali, Juan and Alexandria. Find
where they should be located on the dot plot and put the correct absolute
deviation number to represent each of them.
Step 10 Add the numbers to the left of the 0 on the dot plot. Then add the numbers to
the right of the 0. What do you notice? What does this tell you about the mean
as a “balancing” value for the data set?
Vocabulary
Outlier
An extreme value that varies greatly from the other values in a
data set.
Good to Know!



When analyzing statistics, it is important to take the following into
account: where the data came from, how much data was collected,
how spread out the data is and any clusters that are present.
Outliers can have a large impact on the mean, but little impact on the
median or mode.
Statistics from a larger data set are usually more reliable than statistics
from a smaller data set.
Example 1
Find the mean, median and mode of each data set. Determine
which measure of center best represents each data set.
a. 4, 2, 2, 8, 6, 2, 8, 5, 8
45
Mean =
=5
9
Median = 5
Modes = 2 and 8
Since there is no mode, that would not be the best measure of
center. The mean or median represents the data the best.
Example 1 Continued…
Find the mean, median and mode of each data set. Determine
which measure of center best represents each data set.
b. 18, 19, 12, 17, 1, 19, 19
105
Mean =
= 15
7
Median = 18 Mode = 19
The median best represents this data set. The mean is
affected by the outlier (1) and the mode does not really
represent the middle of the data set.
Example 1 Continued…
Find the mean, median and mode of each data set. Determine
which measure of center best represents each data set.
c. 10, 10, 7, 10, 10, 8, 10, 10, 10, 10
95
Mean =
= 9.5
10
Median = 10 Mode = 10
All three measures of center represent this data set well.
However, when there are many values that are the same, the
mode is the best choice. The mode of 10 best represents this
data set.
Example 2
Jessie and Samantha compared how many movies they watched per
month for a year. The two dot plots show each set of data:
a. Compare the dot plots and describe the differences you see.
Jessie’s dot plot is more spread out than Samantha’s. He has more
low values, but also has some high numbers. Samantha’s dot plot is
symmetrical.
Example 2 Continued…
Jessie and Samantha compared how many movies they watched per
month for a year. The two dot plots show each set of data:
b. Find the measures of center for both Jessie and Samantha.
How do they compare?
Jessie: Mean = 3.5; Median = 2; Mode = 1
Samantha: Mean = 4.5; Median = 4.5; Mode = 4, 5
Jessie’s measures of center are lower than Samantha’s.
Example 2 Continued…
Jessie and Samantha compared how many movies they watched per
month for a year. The two dot plots show each set of data:
c. Find the range for each data set. How do they compare?
Jessie’s Range = 11 – 0 = 11
Samantha’s Range = 7 – 2 = 5
Jessie’s values are much more spread out.
Example 2 Continued…
Jessie and Samantha compared how many movies they watched per
month for a year. The two dot plots show each set of data:
d. Which person is likely to watch more than 4 movies in a month?
Which is more likely to watch more than 7 movies in a month?
Samantha is more likely to watch more than 4 movies in a month.
Samantha did this six out of the twelve months compared to Jessie,
who watched more than 4 movies only three times.
Jessie is more likely to watch more than 7 movies in a month.
Samantha never watched more than 7 movies in a month.
Communication Prompt
Which measure of center is typically used by teachers to
calculate your grade in a class? If you got to choose
which measure of center was used for calculating
grades, which would you choose? Why?
Exit Problems
1. Find the mean, median and mode of the following data set.
17, 18, 13, 15, 3, 11, 20, 18, 14
mean = 14.3; median = 15; mode = 18
2. Which measure of center best represents the data in #1?
Explain.
Since the outlier (3) affects the mean, the median
probably best represents the data.