INTRODUCTION TOSTATISTICS FOR ALGEBRA IS-ID.1Represent data with histograms and boxplotsS-ID.2Use statistics appropriate to theshape of the distributionS-ID .3Interpret difference in shape, center andspread 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 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
Displaying Quantative data• Distribution of quantative data and be able to analyze center, spread and shape• Dot Plots• Stem Plots• Histograms• Box plots
• Label axes and title graphDot Plots • Scale the axis on the values of datanum • 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?
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
HistogramsStemplot displays the actual dataHistograms – breaks thevalues into ranges of valuesand displays the counts orpercent of observations Classes or bars must be the same width The calculator can help you graph a histogram
Box plotsBoxplots are based on thefive number summary anduseful for comparing twoor more distributionsA central box spans thequartiles 1 and 3A line in the box marks themedianLines extend from the boxout to the smallest andlargest 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 HighwayAcura NSX 17 24Audi TT Roadster 20 28BMW Z4 Roadster 20 28 Construct boxCadillac XLR 17 25 plotsChevrolet CorvetteDodge Viper 18 12 25 20 to analyze theFerrari 360 Modena 11 16 data.Ferrari Maranello 10 16 Write a briefFord Thunderbird 17 23Honda Insight 9 15 description comLamborghini Gallardo 9 13 paring the twoLotus Esprit 15 22Maserati Spyder 12 17 types of cars.Mazda Miata 22 28Mercedes-Benz SL500 16 23Mercedes-Benz SL600 13 19Nissan 350Z 20 26Porsche Boxster 20 29Porsche Carrera 911 15 23Smart Pure Coupe 34
Two Seater carsCalculate the mean and median of the city and highway milesper gallonWhich value best describes the typical amount of miles pergallon?
S-ID .3 Interpret difference in shape, center and spread in context of data sets1. Understand why distributions take on particular shapes2. Understand the higher the value of a measure of variabilitythe more spread out the data set is3. Explain the effect of any outliers on the shape, center andspread of the data sets.
Types of distributions1. Understand why distributions take on particular shapesGive an example of a distribution that would be skewed to theright?Give an example of a distribution that would be skewed to theleft?
1. Understand why distributions take on particular shapesWhy does the shape of the distribution of incomes forprofessional athlets tend to be skewed to the right?Why does the shape of the distribution of test scores on a reallyeasy test tend to be skewed to the left?Why does the shape of the distribution of heights of thestudents at your school tend to be symmetrical?
2. Understand the higher the value of a measure ofvariability the more spread out the data set isOn the last weeks math test. Mrs. Wasco class had an averageof 83 points with a standard deviation of 8 points. Mrs. Ruggerios class had an average of 78 points with astandard devaition of 4 points. Which class was moreconsistent with their test scores? How do you know?
3. Explain the effect of any outliers on theshape, center and spread of the data sets.The heights of Monroe High school basketball playersare 5ft 9in; 5 ft 4 in; 5 ft 6 in; 5 ft 5 in; 5 ft 3 in; 5 ft 7 inA students transfers to Monroe High and joins thebasektball 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 newstudent and without the new student.
What is the mean height before the new playertransfer in? ______ What is the median?_____What is the mean height after the new playertransfers in? ______ What is the median?_______What affect does new players height have on theteams height distribution and why?How many players are taller than the new meanteam height?Which measure of center most accurately describesthe teams average height? explain