INTRODUCTION TO STATISTICS FOR ALGEBRA I

S-ID.1 Represent data with histograms and box plotsS-ID.2 Use statistics appropriate to the shape of the distributionS-ID .3Interpret difference in shape, center and spread in context of data sets

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

Displaying Categorical data

• Distribution of categorical data in either counts or percent of individuals

• Bar graphs and Segmented Bar graphs

• Pie Charts

Activity: Heart rate

• A persons pulse provides information about their healtho Count the number of pulse beats in one

minuteo Do this three times and calculate your

average pulse rateo Record your rates on the board

Females and males

Displaying Quantative data

• Distribution of quantative data and be able to analyze center, spread and shape

• Dot Plots• Stem Plots• Histograms• Box plots

Dot Plots• Label axes and title graph• Scale the axis on the values

of data• 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 members from your classmates

num

What can you see about the family members in your class?

 

Number of hours of sleep

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 bottomo 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

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

Box plots

Boxplots are based on the five number summary and useful for comparing two or more distributionsA central box spans the quartiles 1 and 3A line in the box marks the medianLines extend from the box out to the smallest and largest observations

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

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

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

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

Two Seater CarsModel City Highway

Acura NSX 17 24

Audi TT Roadster 20 28

BMW Z4 Roadster 20 28

Cadillac XLR 17 25

Chevrolet Corvette 18 25

Dodge Viper 12 20

Ferrari 360 Modena 11 16

Ferrari Maranello 10 16

Ford Thunderbird 17 23

Honda Insight 9 15

Lamborghini Gallardo 9 13

Lotus Esprit 15 22

Maserati Spyder 12 17

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

Construct box plots to analyze the data.  Write a brief description comparing the two types of cars. 

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?

S-ID .3Interpret 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.

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?

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?

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?

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.

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