1. INTRODUCTION TO
STATISTICS FOR ALGEBRA I
S-ID.1
Represent data with histograms and box
plots
S-ID.2
Use statistics appropriate to the
shape of the distribution
S-ID .3
Interpret difference in shape, center and
spread in context of data sets

2. Variables
• Categorical variable – records which of
several groups or categories an
individual belongs (Qualitative
Variable)
• Quantitative Variable – numerical
values for which it makes sense to do
arithmetic operations

3. Displaying Categorical data
• Distribution of categorical data in either
counts or percent of individuals
• Bar graphs and Segmented Bar graphs
• Pie Charts

4. Activity: Heart rate
• A persons pulse provides information
about their health
o Count the number of pulse beats in one
minute
o Do this three times and calculate your
average pulse rate
o Record your rates on the board
 Females and males

5. Displaying Quantative data
• Distribution of quantative data and be
able to analyze center, spread and
shape
• Dot Plots
• Stem Plots
• Histograms
• Box plots

6. • Label axes and title graph
Dot Plots
• Scale the axis on the values
of data
num
• Mark a dot above the
number on the horizontal
axis corresponding to each
data value
• Activity: Construct a dot plot
of the number of family
Number of hours of sleep members from your
classmates
What can you see about the family members in
your class?

7. Stem plot
• Separate each observation into a stem
consisting of all but the rightmost digit
and a leaf, the final digit
• Write stems vertically in increasing order
from top to bottom
o Draw vertical line to the right of the
stem
• Rearrange the leaves in increasing order
from the stem
• Title your graph and add a key describing
what the stem and leaves are
• Construct a stem plot of the data of the
blood pressures of the class

8. Histograms
Stemplot displays the actual data
Histograms – breaks the
values into ranges of values
and displays the counts or
percent of observations
Classes or bars must be
the same width
The calculator can help you
graph a histogram

9. Box plots
Boxplots are based on the
five number summary and
useful for comparing two
or more distributions
A central box spans the
quartiles 1 and 3
A line in the box marks the
median
Lines extend from the box
out to the smallest and
largest observations

10. Five number summary
• Minimum
• Q1
• Median
• Q3
• Maximum
• Offers a reasonably complete description of center and
spread using median
• Box plot is a graph of a five number summary
• Modified Boxplot graph of five number summary with
outliers plotted individually
Modified
Regular Boxplot

11. Graphing a Histogram
- using the graphing calculator
• Type the data into List 1
• Go to the StatPlot Menu
o set plot ON and choose histogram
• Set your
o (Xscl is the size of the bars)
• Choose
• Use to read the number of observations
in each category

12. Graphing a Box plot -
using the graphing calculator
• Enter Data into List 1
• Go to the StatPlot Menu
o set the plot ON and choose boxplot
• You can either go to and choose
an appropriate window for the data OR
• Use the Trace key to read the 5-number summary for the
data.
Note: You can graph up to 3 boxplots at teh
same time - just use Plot2 & Plot 3. When in TRACE,
use the up down arrows to switch between plots

13. Presentation of data (review)
• Bar chart – compares the sizes of the groups or
categories
• Pie Chart – Compares what part of the whole the
group is
• Dotplots – Compares the range of the data and its
variables
• Histogram – graphing one quantitative variable in
groups
• Stemplot – organizes and groups data but allows us
to see as many of the digits in each data value as we
wish
• Box plots – organizes data in quartiles to divide data

14. Two Seater Cars
Model City Highway
Acura NSX 17 24
Audi TT Roadster 20 28
BMW Z4 Roadster 20 28
Construct box
Cadillac XLR 17 25 plots
Chevrolet Corvette
Dodge Viper
18
12
25
20
to analyze the
Ferrari 360 Modena 11 16 data.
Ferrari Maranello 10 16 Write a brief
Ford Thunderbird 17 23
Honda Insight 9 15
description com
Lamborghini Gallardo 9 13 paring the two
Lotus Esprit 15 22
Maserati Spyder 12 17
types of cars.
Mazda Miata 22 28
Mercedes-Benz SL500 16 23
Mercedes-Benz SL600 13 19
Nissan 350Z 20 26
Porsche Boxster 20 29
Porsche Carrera 911 15 23
Smart Pure Coupe 34

15. Two Seater cars
Calculate the mean and median of the city and highway miles
per gallon
Which value best describes the typical amount of miles per
gallon?

16. S-ID .3
Interpret difference in shape, center and
spread in context of data sets
1. Understand why distributions take on particular shapes
2. Understand the higher the value of a measure of variability
the more spread out the data set is
3. Explain the effect of any outliers on the shape, center and
spread of the data sets.

17. Types of distributions
1. Understand why distributions take on particular shapes
Give an example of a distribution that would be skewed to the
right?
Give an example of a distribution that would be skewed to the
left?

18. 1. Understand why distributions take on particular shapes
Why does the shape of the distribution of incomes for
professional athlets tend to be skewed to the right?
Why does the shape of the distribution of test scores on a really
easy test tend to be skewed to the left?
Why does the shape of the distribution of heights of the
students at your school tend to be symmetrical?

19. 2. Understand the higher the value of a measure of
variability the more spread out the data set is
On the last week's math test. Mrs. Wasco class had an average
of 83 points with a standard deviation of 8 points.
Mrs. Ruggerio's class had an average of 78 points with a
standard devaition of 4 points. Which class was more
consistent with their test scores? How do you know?

20. 3. Explain
the effect of any outliers on the
shape, center and spread of the data sets.
The heights of Monroe High school basketball players
are 5ft 9in; 5 ft 4 in; 5 ft 6 in; 5 ft 5 in; 5 ft 3 in; 5 ft 7 in
A students transfers to Monroe High and joins the
basektball team. Her height is 6 ft 10 in.
How would you find the mean and median of the data sets?
Find the median and mean of the data sets with the new
student and without the new student.

21. What is the mean height before the new player
transfer in? ______ What is the median?_____
What is the mean height after the new player
transfers in? ______ What is the median?_______
What affect does new players height have on the
team's height distribution and why?
How many players are taller than the new mean
team height?
Which measure of center most accurately describes
the team's average height? explain