# UNF STA 2023 - Displaying and Exploring Data (36 pages)

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## Displaying and Exploring Data

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- Pages:
- 36
- School:
- University of North Florida
- Course:
- Sta 2023 - (GM) Elementary Statistics for Business

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Describing Data Displaying and Exploring Data Chapter 4 McGraw Hill Irwin The McGraw Hill Companies Inc 2008 GOALS 2 Develop and interpret a dot plot Develop and interpret a stem and leaf display Compute and understand quartiles deciles and percentiles Construct and interpret box plots Compute and understand the coefficient of skewness Draw and interpret a scatter diagram Construct and interpret a contingency table Dot Plots 3 A dot plot groups the data as little as possible and the identity of an individual observation is not lost To develop a dot plot each observation is simply displayed as a dot along a horizontal number line indicating the possible values of the data If there are identical observations or the observations are too close to be shown individually the dots are piled on top of each other Dot Plots Examples Reported below are the number of vehicles sold in the last 24 months at Smith Ford Mercury Jeep Inc in Kane Pennsylvania and Brophy Honda Volkswagen in Greenville Ohio Construct dot plots and report summary statistics for the two small town Auto USA lots 4 Dot Plot Minitab Example 5 Example Dot Plots of Vehicle Sales Notice that the scales for the side by side dot plots differ This means that we need to be careful in comparing the two plots The distribution of monthly counts for Brophy Honda Volkswagen is shifted to the right relative to the distribution for Smith Ford Mercury Jeep Inc 6 Stem and Leaf 7 In Chapter 2 we showed how to organize data into a frequency distribution The major advantage to organizing the data into a frequency distribution is that we get a quick visual picture of the shape of the distribution One technique that is used to display quantitative information in a condensed form is the stem and leaf display Stem and leaf display is a statistical technique to present a set of data Each numerical value is divided into two parts The leading digit s becomes the stem and the trailing digit the leaf The stems are located along the vertical axis and the leaf values are stacked against each other along the horizontal axis Advantage of the stem and leaf display over a frequency distribution the identity of each observation is not lost Stem and Leaf Example Suppose the seven observations in the 90 up to 100 class are 96 94 93 94 95 96 and 97 The stem value is the leading digit or digits in this case 9 The leaves are the trailing digits The stem is placed to the left of a vertical line and the leaf values to the right The values in the 90 up to 100 class would appear as Then we sort the values within each stem from smallest to largest Thus the second row of the stemand leaf display would appear as follows 8 Stem and leaf Another Example Listed in Table 4 1 is the number of 30 second radio advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association last year Organize the data into a stem and leaf display Around what values do the number of advertising spots tend to cluster What is the fewest number of spots purchased by a dealer The largest number purchased 9 Stem and leaf Another Example 10 Example ATM Usage in Hawaii Aloha Banking Co is studying ATM use in suburban Honolulu A sample of 30 ATM s was selected and data were collected on the number of times each ATM was used on a certain day We want to study the characteristics of the distribution of daily ATM usage What is the minimum Maximum Median 11 Quartiles Deciles and Percentiles 12 The standard deviation is the most widely used measure of dispersion Alternative ways of describing spread of data include determining the location of values that divide a set of observations into equal parts These measures include quartiles deciles and percentiles Percentile Computation 13 To formalize the computational procedure let Lp refer to the location of a desired percentile So if we wanted to find the 33rd percentile we would use L33 and if we wanted the median the 50th percentile then L50 The number of observations is n so if we want to locate the median its position is at n 1 2 or we could write this as n 1 P 100 where P is the desired percentile Percentiles Example Listed below are the commissions earned last month by a sample of 15 brokers at Salomon Smith Barney s Oakland California office Salomon Smith Barney is an investment company with offices located throughout the United States 2 038 2 097 2 287 2 406 1 758 2 047 1 940 1 471 1 721 1 637 2 205 1 787 2 311 2 054 1 460 Locate the median the first quartile and the third quartile for the commissions earned 14 Percentiles Example cont Step 1 Organize the data from lowest to largest value 1 460 1 758 2 047 2 287 15 1 471 1 787 2 054 2 311 1 637 1 940 2 097 2 406 1 721 2 038 2 205 Percentiles Example cont Step 2 Compute the first and third quartiles Locate L25 and L75 using 25 75 L25 15 1 4 L75 15 1 12 100 100 Therefore the first and third quartiles are the 4th and 12th observation in the array respectively L25 1 721 L75 2 205 16 Another Measure of Variability The Interquartile Range IQR of a numeric data set is the difference between the third and first quartiles IQR L75 L25 This measure of variability tells the range of values of the middle 50 of the data set The first and third quartiles are sometimes denoted by Q1 L25 and Q3 L75 17 Example ATM Usage Let s look at the spread of the data on Aloha ATM usage using both standard deviation and quartiles If we use MegaStat and choose Descriptive Statistics we may find the quartiles by specifying the Minimum Maximum Range and the Median Quartiles Mode Outliers options Or we may do a stem and leaf plot and locate the quartiles on the graph 18 Boxplots Graphical Use of the 5Number Summary The 5 number summary of a data set consists of the minimum value the first second median and third quartiles and the maximum value of the data We can use these five numbers to construct a simple graph called a boxplot of the data We will compare the characteristics of the boxplot with those of the stem and leaf plot for several data sets including the Whitner Autoplex data and the radio spot data But first another example 19 Boxplot Example 20 Boxplot Example 21 Boxplot Whitner Autoplex Refer to the Whitner Autoplex data in Table 2 4 Develop a box plot of the data What can we conclude about the distribution of the vehicle selling prices What is the shape of the distribution Is it skewed What is the spread using both measures of spread standard deviation and IRQ 22 Boxplot Radio

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