Lesson 1 – 1a from Displaying Distribution with Graphs

Knowledge Objectives What is meant by exploratory data analysis What is meant by the distribution of a variable Differentiate between categorical variables and quantitative variables What is meant by the mode of a distribution What is meant by an outlier in a stemplot or histogram

Construction Objectives Construct bar graphs and pie charts for a set of categorical data Construct a stemplot for a set of quantitative data Construct a back-to-back stemplot to compare two related distributions Construct a stemplot using split stems Construct a histogram for a set of quantitative data, and discuss how changing the class width can change the impression of the data given by the histogram

Construction Objectives cont Describe the overall pattern of a distribution by its shape, center, and spread Recognize and identify symmetric and skewed distributions Construct and interpret an ogive (relative cumulative frequency graph) from a relative frequency table Construct a time plot for a set of data collected over time

Vocabulary Roundoff error – errors associated with decimal inaccuracies Pie chart – chart that emphasize each category’s relation to the whole Bargraph – displays the distribution of a categorical variable Stemplot – includes actual numerical values in a plot that gives a quick picture of the distribution Back-to-back stemplot – two distributions plotted with a common stem Splitting stems – divides step into 0-4 and 5-9 Trimming – removes the last digit or digits before making a stemplot Histogram – breaks range of values into classes and displays their frequencies Frequency – counts of data in a class Frequency table – table of frequencies

Vocabulary Modes – major peaks in a distribution Unimodal – a distribution whose shape with a single peak (mode) Bimodal – a distribution whose shape has two peaks (modes) Symmetric – if values smaller and larger of the center are mirror images of each other Skewed – if smaller or larger values from the center form a tail Ogive – relative cumulative frequency graph Time plot – plots a variable against time on the horizontal scale of the plot Seasonal variation – a regular rise and fall in a time plot

Categorical Data Categorical Variable: –Values are labels or categories –Distributions list the categories and either the count or percent of individuals in each Displays: BarGraphs and PieCharts

Categorical Data Example Body PartFrequencyRelative Frequency Back120.4 Wrist Elbow Hip Shoulder Knee Hand Groin Neck Total Physical Therapist’s Rehabilitation Sample

Categorical Data Items are placed into one of several groups or categories (to be counted) Typical graphs of categorical data: –Pie Charts; emphasizes each category’s relation to the whole –Bar Charts; emphasizes each category’s relation with other categories Pie Chart Bar Chart

Charts for Both Data Types Pareto ChartRelative Frequency Chart Cumulative Frequency Chart

Example 1 Construct a pie chart and a bar graph. Radio Station Formats FormatNr of StationsPercentage Adult contemporary1, Adult standards Contemporary Hits Country2, News/Talk/Info2, Oldies1, Religious2, Rock Spanish Language Other formats1, Total13, Why not 100%?

Example 1 Pie Chart

Example 1 Bar Graph

Quantitative Data Quantitative Variable: –Values are numeric - arithmetic computation makes sense (average, etc.) –Distributions list the values and number of times the variable takes on that value Displays: –Dotplots –Stemplots –Histograms –Boxplots

Dot Plot Small datasets with a small range (max-min) can be easily displayed using a dotplot –Draw and label a number line from min to max –Place one dot per observation above its value –Stack multiple observations evenly First type of graph under STATPLOT 34 values ranging from 0 to 8

Stem Plots A stemplot gives a quick picture of the shape of a distribution while including the numerical values –Separate each observation into a stem and a leaf eg. 14g -> 1| > 25|6 32.9oz -> 32|9 –Write stems in a vertical column and draw a vertical line to the right of the column –Write each leaf to the right of its stem Note: –Stemplots do not work well for large data sets –Not available on calculator

Stem & Leaf Plots Review Given the following values, draw a stem and leaf plot 20, 32, 45, 44, 26, 37, 51, 29, 34, 32, 25, 41, 56 Ages Occurrences | 0, 6, 9, 5 | 3| 2, 3, 4, 2 | 4| 5, 4, 1 | 5| 1, 6

Splitting Stems Double the number of stems, writing 0-4 after the first and 5-9 after second.

Back-to-Back Stemplots Back-to-Back Stemplots: Compare datasets Example1.4, pages Literacy Rates in Islamic Nations

Example 1 The ages (measured by last birthday) of the employees of Dewey, Cheatum and Howe are listed below. a)Construct a stem graph of the ages b)Construct a back-to-back comparing the offices c)Construct a histogram of the ages Office A Office B

Example 1a: Stem and Leaf 2 0, 1, 2, 6, 8, 8, 3 0, 1, 1, 2, 3, 5, 6, 7, 8, 9, 9, 4 2, 2, 5, 7, 8, 9, 9, Ages of Personnel

Example 1b: Back-to-Back Stem 2 0, 8 3 2, 3, 5, 6, 7, 8, 4 5, 7, 8, 9, Office B: Ages of PersonnelOffice A: Ages of Personnel 1, 2, 6, 8 0, 1, 1, 9, 9 2, 2, 9

Example 2 Below are times obtained from a mail-order company's shipping records concerning time from receipt of order to delivery (in days) for items from their catalogue? a)Construct a stem plot of the delivery times b)Construct a split stem plot of the delivery times c)Construct a histogram of the delivery times

Example 2: Stem and Leaf Part 0 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9 1 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 9 2 1, 2, 2, 3, 5, Days to Deliver

Example 2b: Split Stem and Leaf 0 2, 3, 3, 4 0 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9 1 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, , 2, 2, 3 2 5, Days to Deliver

Day 1 Summary and Homework Summary –Categorical data Data where adding/subtracting makes no sense Pie charts and bar graphs –Quantitative data Data where arithmetic operations make sense Stem plots and histograms –Some graphs can work for both types of data Frequency and dot plots Ogive and Pareto Homework –pg 46 – 48 problems 1-5