CH 2 Frequency Distributions and Graphs PDF

CH 2: FREQUENCY DISTRIBUTIONS AND GRAPHS Qualitative (Categorical) Data 2.1 For this section we will use the following raw data that represent the blood types for 25 persons A B B AB O O O B AB...

CH 2: FREQUENCY DISTRIBUTIONS AND GRAPHS Qualitative (Categorical) Data 2.1 For this section we will use the following raw data that represent the blood types for 25 persons A B B AB O O O B AB B B B O A O A O O O AB AB A O B A a) Make a Categorical Frequency Table b) Construct a Pie graph c) Construct a Bar chart d) Construct a Pareto chart a) Making a Categorical Frequency Table Enter the given data into C1 and name the column “B- "TYPE Step 1. Select Stat˃ Tables˃ Tally Individual Values  Step 2. Make the "Variables" window active (Place cursor inside the window and click). Then Double-click C1 B-TYPE Step 3. Check the boxes for the :Display Counts, Percents, Cumulative ,counts and Cumulative percents Step 4. Click OK The categorical frequency table is displayed in the session window b) Construct a Pie chart Step 1. Click on Graph˃ Pie Chart Step 2. Click on the inside of the Categorical variables box, "double click "C1 B-TYPE Step 3. Click on Labels box In the Titles/Footnotes tab enter a title and a subtitle1 for the chart. "" Pie Chart", and "Blood Types In the Footnote1/Footnote2 enter.your name and your id number  Click on the Slice Labels tab Check on all boxes and click OK Step 4. Click OK The pie chart is displayed in the graph window b) Construct a Bar chart Step 1. Click on Graph˃ Bar Chart˃ Simple˃ OK  Step 2. Click on the inside of the Categorical variables box, double click "C1 B- "TYPE Step 3. Click on Labels box In the Titles/Footnotes tab enter a title ,"and a subtitle1 for the chart. " Bar Chart "and "Blood Types In the Footnote1/Footnote2 enter your.name and your id number Click on the Data Labels tab Check on Use y-value labels and click OK Step 4. Click OK The Bar chart is displayed in graph window A Bar chart of Relative Frequencies (or percent) can be created from a Frequency :Bar chart as follows Click on Graph˃ Bar Chart˃ Simple˃ OK Click on Chart Options box In the Percent and Accumulative box, check on Show Y as Percent, click OK Click OK.The y-axis labels changed to percent c) Construct a Pareto chart Step 1. Click on Stat˃ Quality Tools˃ Pareto Chart Step 2. Click the option to Chart defects data in, and double click "C1."B-TYPE Step 3. Click OK The Pareto chart is displayed in the graph window Note: The cumulative percent chart will disappear By doing the following  Step 1. Click on Stat˃ Quality Tools˃..…Pareto Chart˃ Options Step 2. Click "Do not chart "cumulative percent Option Step 3. Click OK and OK The cumulative percent chart.disappeared If the data are provided as a table :Consider the following table Attitude Toward Statistics Attitude Number of students Love 23 Like 46 Indifferent 9 Hate 12 a) Construct a Pie chart Enter the Attitude in C1, and the.1.Number of students in C2  Click on Graph˃ Pie Chart.2 Click on Chart values from table.3 Click on the inside of the.4 Categorical variables box ;Double-click on the C1- Attitude.5 C1 is placed inside the box Click on the inside of the.6 Summary variables box Double-click the column that contains.7 ;the frequencies:C2 Number of students the column is placed inside the box Click on the Labels box.8 In the Titles/Footnotes tab enter a.9 title and subtitle for the chart: "Pie ,"Chart "and "Attitude Toward Statistics In the Footnote1/Footnote2.10 enter your.name and your id number.11 Click on the Slice Labels tab Check on all boxes and click OK.12 Click OK again.13  The pie chart is displayed in the graph window b) Construct a Bar chart Click on Graph˃ Bar Chart In the Bars represent box select Values from a table option Select Simple Click Ok Click on the inside of the Graph variables Double-click the column that contains the frequencies: C2- Number of ;students the column is placed inside the box Click on the inside of the Categorical variable box Double-click on the column C1 – Attitude ; C1 Attitude is placed inside the box  Click on the Labels box In the Titles/Footnotes tab enter a title ,"and a subtitle for the chart: "Bar Chart."and "Attitude Toward Statistics In the Footnote1/Footnote2 enter your name and your id number Click OK Click on the Data Labels tab Check on Use y-value labels and click OK Click OK again The bar chart is displayed in the ☺ graph window A Bar chart of Relative Frequencies (or percent) can be created from a :Frequency Bar chart as follows Click on Chart Options box ,In the Percent and Accumulative box check on Show Y as Percent, click OK Click OK again  LAB ACTIVITIES FOR CATEGORICAL DATA :The following data represent the housing arrangements for 25 people.1 H = House, A = Apartment, M = Mobile home, C = Condominium H C H M H C C M C C A C A C C H A H H C M C A M A Make a Categorical Frequency Table (a) Construct a Pareto chart (b) Construct a Pie graph (c) Construct a frequency Bar chart (make sure to label the columns) (d) Construct a relative frequency Bar chart (make sure to label the (e) columns) Explain your finding (f) Reason We Travel The following data are based on a survey from.2.American Travel Survey on why people travel Purpose Number Personal business 146 Visit friends or relatives 330 Work-related 225 Leisure 299 Construct a Pie graph (a) Construct a frequency Bar chart (make sure to label columns) (b) Construct a relative frequency Bar chart (make sure to label columns) (c) Construct a Pareto chart (d) Analyze the results (d)  Quantitative Data 2.2 Discrete Case: for this case we will use the following raw data that represent items purchased at a convenience store by 30 randomly selected.customers 8 3 5 7 5 6 8 2 6 6 3 4 9 2 6 7 1 2 4 9 8 9 9 6 4 2 3 2 6 4 a) Make an Ungrouped Frequency Table b) Construct a Histogram c) Construct a Frequency Polygon d) Construct an Ogive (cumulative frequency polygon) a) Making an Ungrouped Frequency Table ”Enter the given data into C1 and name the column “NO. OF ITEMS Step 1. Select Stat > Tables > Tally Individual Variables Step 2. Make the “Variables” window active.(Place cursor inside the window and click).Then Double-click C1 NO. OF ITEMS :Steop3. Check the boxes for the Display Counts, percents, Cumulative count, and Cumulative percents Step 4. Click OK The ungrouped frequency table is displayed In the session window b) Construct a Histogram Step 1. Click Graph > Bar Chart > Simple>OK Step 2. Click on the inside of the Categorical  variables box, double click ”C1 NO. OF ITEMS" Step 3. Click on Labels box In the Titles/Footnotes tab enter a title and a subtitle1 for the chart. "“Histogram”, and "NO. OF ITEMS In the Footnote1/Footnote2 enter.your name and your id number Click on the Data Labels tab Check on Use y-value labels and click OK  Step 4. Click OK The Bar chart is displayed in graph window We will adjust this Bar graph into Histogram by removing the gaps between.bars.Now, double click anywhere on x-axis. The following dialogue box appears Uncheck Gap option and enter.0 for Gap between clusters, then OK The following Frequency Histogram will be.displayed A Histogram of Relative Frequencies (or percent) can be done from a :Frequency Histogram as follows Double click anywhere inside the histogram. The following dialogue box appears  Click on Chart Options tab In the Percent and Accumulate options select Show Y as Percent, then OK The following Relative Frequency Histogram will.displayed c) Construct a Frequency Polygon Click on Graph > Bar Chart> Simple > OK Click on the Data Labels tab Check on Use y-value labels and click OK Click the Data View box In the Data Display tab uncheck Bars option and select Symbols and.Connect line options  Click OK and OK.The following Frequency Polygon will be displayed Note: Make sure to change the.title of the graph to be Frequency Polygon d) Construct an Ogive (Cumulative Frequency Polygon) :An Ogive can be done from a Frequency Polygon as follows Double click anywhere on the frequency polygon graph. The following dialogue box appears Click on Chart Options tab In the Percent and Accumulate options select Accumulate Y across X,.then OK.The following Frequency Ogive will be displayed Note: Make sure to change the title of the graph to be.Frequency Ogive For the a Relative Frequency Ogive (percent) select the Show Y as percent.option in Chart Options tab LAB ACTIVITIES FOR DISCRETE DATA BUN Count The blood urea nitrogen (BUN) count for 20 randomly selected.patients is given here in milligrams per deciliter (mg/dl) 18 13 20 11 17 12 14 13 18 17 22 19 15 16 12 17 16 14 17 19 :a) Make an ungrouped frequency table to answer the following questions What percent of patients whose BUN is less than 17 - What percent of patients whose BUN is at least 16 - What percent of patients whose BUN is greater than 18 - What percent of patients whose BUN is at most 15 - What percent of patients whose BUN is between 17 and 20 (inclusive) - What percent of patients whose BUN is at least 12 - What percent of patients whose BUN is 19 - What percent of patients whose BUN is at most 22 - b) Construct a frequency histogram c) Construct a relative frequency (percent) histogram d) Construct a frequency polygon e) Construct a relative frequency (percent) polygon f) Construct frequency ogive g) Construct a relative frequency (percent) ogive Continuous case: For this case we will use the following raw data that represent the record high temperatures in degrees Fahrenheit for each of the 50