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# Chapter 2.2 & 2.3 Stat 200

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This page Class Notes was uploaded by Ayana Smith on Tuesday February 2, 2016. The Class Notes belongs to Stat 200 at Radford University taught by Dr. Kirtner in Spring 2015. Since its upload, it has received 18 views. For similar materials see Statistics 200 in Math at Radford University.

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Date Created: 02/02/16

StatZOU Sections 2223 39 Graphical Displays of Data i 33 L IN light I a 39 I In section 21 we discussed that a as which prowde useful visual display ofthe y or a a in section 22 t 7 data A u g as y 39quot it 3 in distribdtion of data With histogramsf the data must be we discuss other types of graphs which are suitable for l Graphs That are Used to Summarize Qualitative Data A Bar Graphs show the amount of data belongs to each category as proportionally sized rectangular areas there are spaces between the bars It is used to display 7 i 39 ri sgjata that is counted or broken into percentages This graph displays each category with respect to other categories Example The table below lists the number of automobiles sold last week by day for a local dealership Describe the data using a bar graph Day Number Sold Monday 7 I 15 Tuesday 23 Wednesday 7 3 5 Thursday 7 11 Friday 12 Saturday 7 42 Solution BAR GRAPH Automobiles Sold Last Week Frequency H M M Lu 3 U D In C DU39I Mmda l TUESdaV WEdeSday Thursday Friday Saturday DayofWeek B Pareto charts A pareto chart is a l liniWh39Ch the bar halght to represents frequency of an event In addition the bars are arranged llquot 3 according tog Example Data from Automobiles sold last week in previous example Solution Pareto Chart Automobiles Sold Last Week Frequency Saturday Wednesday Tuesday Monday Friday Thursday DayofWeek 2 Circle Graphs or Pie Charts in a circle graph or pie chart wedges of a circle visually display proportional parts ofthe total that share a common characteristic 5 Example Using Automobile Data from before 7 Day Number Sold Relative Frequency Monday 7 15 Elt l 39 7 Tuesday 23 27 tall Wednesday 35 293 Thursday 11 V 1 1 Friday 12 2 CH Saturday 42 dealtEgg Ell 39i Elfr l Solution Begin by finding the relative frequency or percent of each category Then construct the pie chart using the relative frequencies in terms of percentages Automobiles Sold Last Week ta flgii mam Questions 1 Which day has the largest number of sales 2 The least Timers th 39 3 On which two days are more than 50 ofthe cars sold ll Graphs That are Usedto Summarize Quantitative Data A Histograms discussed previously B TimeSeries Graphs A times series graph is a graph showing data measurements in W i quotiquot is Time is on the horizontal scale and the variable being measured is on the vertical scale We connect the data points by line segments Data is plotted at in order of occurrence at regular intervals over a period of Examp le The table lists the number of cellular telephone subscribers in millions and a subcriber s average local monthly bill for service in dollars for the i rears 1995 through 2005 Construct a time series chart for the number of cellular subscribers What can you conclude rr ifear Subscribers in millions Average bill in dollars 1995 338 5100 1996 440 4770 1997 553 4278 1999 692 9943 1999 860 4124 2000 1095 4527 2001 1284 4737 2002 1408 4840 2003 7 1587 4991 2004 1821 5064 7 2005 2079 4998 Solution Let the horizontal axis represent the years and the vertical axis represent the number of subscribers in millions Then plot the paired data and connect them with line segments 250 200 150 100 50 Number of Cellular Telephone Subscribers in millions for the Years 19952005 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 C Ogives An ogive is a graph that represents imt llmhl l t rl frequencies or CU t tm flist relative freq uencies For example if vet saved 306 in both Eanaarv and ater and 188 in each of February March May and Edna arr ogive would leek like Figdre it Figure 2 Ggive of accumulated savings fer One veer An ogive displays a reading fetal D Stem andLeaf Displays Unlike histograms which lose individual data points stemmandwleaf displays do not Stemeand leaf displays uses the actual digits that make up the data values Each numerical data is divided into two parts The leadin digits becomes the and the trailing digitls becomes the The stems are located along the main axis and a leaf for each piece of data is located so as to display the distribution of the data The scale MUST be listed on the display Example 1 A city police officer using radar checked the speed of cars as they were traveling down the main street in town Construct a stem and leaf plot for this data 41 31 33 35 36 37 39 19 33 19 26 27 24 32 4O 39 16 55 38 36 Solution You can use your calculator to enter the data Calculator Instructions To enter data StatgtEditgtchoose a list and enter data To sort data la la iiiW Statgt2sortAl1gt E d VGA Lg a l frx We get the following list of data 16 l 19 2amp7 254 27 V31 3 32 33 33 35 36 36 2 M 23 than 319 i quot1 3 3 ifquot to 63 WE it P L l to C Q C37 til To make a stem and leaf di5plav draw a vertical column from smallest to largest Draw a is V 39 n x a Mari at vertical line to the right of all the stems Place all the leaves with the same stem in the same row as the stem and arrange the leaves in increasing order Use a label to indicate the magnitude of the number in the display We use a decimal position in the label rather than with the stems or leaves Example 2 The scores for the first round of a golftournament are indicated below Make a a stem and leaf display Use two lines per stern called a double line stem and ieof dispioy Be sure to indicate the scale 771 65 67 73 74 73 43 17th 74 73 w71u 70 75 3971 72 39e7 s 75 7s 71 7e 74 7s 66 75 75 75 W7 72 72 73 as 67 or 5 o N eta 39Md tb v 3 a 4 ll wl Summary ofglmportant Notes Mattieti quoti 39 m39 I iiiX quotquot3 GI fh E ll el iitaEritreaKy 0 M toils A Good graphing requirements All good graphs have some common traits Oi trL lri i e t G They have a descriptive and clear Ell are labeled and titled and are not used to mislead 1 graph break symbol is used to inform the reader will have a consistent scale If the scale does not start at zero a Graphs have a reasonable amount of color or pattern to identify important factors or delineate categories but not too much to di i the reader B Which graph do you use Quantitative data was ii Histogram used with quantitative data to display distributions groupings gsmgquot andKor outliers These can be used with very large data sets Original data is lost Stem 8 Leaf used with quantitative data to display distributions groupings andor outliers These can only be used with small data sets less than a few hundred data items Time Series used to show how data changes over time Qgive used to show cumulative data Qualitative Data Circle Pie Graph used to display qualitative data this is counted or broken into percentages This graph displays each category with respect to the total Bar Graph used to display qualitative data that is counted or broken into percentages This graph displays each category with respect to other categories Pareto Graph used to display qualitative data that is counted or broken into percentages This graph displays each category in decreasing order Which graph do I use Example I have the average gross earnings for Apple Inc for each ofthe last 24 mgnths What graph do i use 7 l WW 5slti fr Example I need to convince my principal that more moneyr needs to be dedicated to purchasing school supplies so i want to do a graph of the wt of kids on free lunch reduced lunch and breakfast and those not needing this service What graph do I use x ca wE gimr v aquot finwrquot K l l

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