6-5 Describing Distributions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
6-5 Describing Distributions
Warm Up
Find the median of each data set
1. 9, 6, 14, 16, 5, 29, 1
9
2. 7, 11, 2, 18, 7, 28, 83, 7
9
3. 9.1, 6.4, 4.2, 5.5, 3.3, 6.3
5.9
6-5 Describing Distributions
Problem of the Day
The following set shows the ages of the nine
incoming U.S. presidents inaugurated during the
second half of the 20th century.
62, 43, 55, 46, 61, 52, 69, 67, 46
What is the median age?
55 years old
What is the mode?
46 years old
6-5 Describing Distributions
Learn describe and compare data
distributions by their center, spread, and
shape, using box-and-whisker plots or dot
plots.
6-5 Describing Distributions
Recall that a frequency distribution is a display that
shows how many times data values fall into
categories of quantity. Frequency distributions are
categorized by their general shape.
Shapes of a Distribution
Skewed
Data are not symmetric
about the center.
Normal
Data are symmetric
about the center.
The measures of center
may not be equal.
The measures of center
are equal.
6-5 Describing Distributions
Additional Example 1: Displaying Distributions on
Dot Plots
A. The data set and dot plot display heart rate
data. Describe the shape of the data
distribution. 85, 84, 83, 82, 85, 80, 84, 90, 87,
85, 86, 88, 86, 85
The data is symmetrical about the center. It shows a
normal shape of distribution.
6-5 Describing Distributions
Continued: Example 1
B. The data set and dot plot display students’
quiz scores. Describe the shape of the data
distribution. 10, 8, 7, 9, 10, 9, 9, 7, 8, 9, 6, 8
The data is skewed. The mean, median, and mode
are varied.
6-5 Describing Distributions
Check It Out: Example 1
The data set and dot plot display the number of
miles Danny ran each day. Describe the shape of
the data distribution.
The data is skewed. The mean, median, and mode
are varied.
6-5 Describing Distributions
Additional Example 2: Displaying Distributions on
Box-and-Whisker Plots
A. The data set and box-and-whisker plot display
the weights in kilograms of 12 cats. Describe the
shape of the data distribution.
5, 2, 6, 4, 6, 3, 4, 9, 3, 5, 3, 4
The data is skewed. The mean, median, and mode
are varied.
6-5 Describing Distributions
Check It Out: Example 2
The data set and box-and-whisker plot display
the number of pets that several students in Ms.
Snow’s class own. Describe the shape of the
data distribution.
9, 0, 4, 1, 1, 2, 3, 5, 2
The data is skewed. The mean, median, and mode
are varied.
6-5 Describing Distributions
Additional Example 3: Comparing Distributions
using Box-and-Whisker Plots
The box-and-whisker plots show the distribution
of cars sold each day on two lots in a month.
What conclusions can you make about the data?
In general, more cars were sold each day in Lot A
than in Lot B. The spread of the data is greater for
Lot B, which means that there is more variation in
the data. The number of cars sold in Lot A is more
predictable than the number of cars sold in Lot B.
6-5 Describing Distributions
Check It Out: Example 3
The box-and-whisker plots show the distribution
of cars sold each day on two lots in a month.
What conclusions can you make about the data?
In general, more cars were sold each day in Lot B than
in Lot A. The spread of the data is greater for Lot B,
which means that there is more variation in the data.
The number of cars sold in Lot A is more predictable
than the number of cars sold in Lot B.
6-5 Describing Distributions
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
6-5 Describing Distributions
Lesson Quiz
1. The data set and dot plot display the number of pets
owned by 14 children. Describe the shape of the data
distribution.
skewed
6-5 Describing Distributions
Continued Lesson Quiz
2. The data set and box-and-whisker plot display the
number of seconds it takes 14 sports cars to reach a
speed of 60 miles per hour. Describe the shape of the
data distribution.
normal
6-5 Describing Distributions
Lesson Quiz For Student Response Systems
1. The dot plot displays the number of pets owned by14
children. Describe the shape of the data distribution.
A. skewed
B. normal
6-5 Describing Distributions
Continued: Lesson Quiz for Student Response
Systems
2. The box-and-whisker plot displays the number of
songs 14 people downloaded per month. Describe the
shape of the data distribution.
A. skewed
B. normal