{"id":390,"date":"2022-06-17T16:51:29","date_gmt":"2022-06-17T16:51:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=390"},"modified":"2022-06-17T16:51:39","modified_gmt":"2022-06-17T16:51:39","slug":"displaying-categorical-data-what-to-know-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/displaying-categorical-data-what-to-know-3\/","title":{"raw":"Displaying Categorical Data: What to Know 3","rendered":"Displaying Categorical Data: What to Know 3"},"content":{"raw":"

Bar Graphs<\/h2>\r\nOne of the most commonly used graphs for visualizing the distribution of a categorical variable is a bar graph. In a bar graph<\/strong>, categories are represented by bars that are separated from each other. The bars can be vertical or horizontal, and the height (or length) of each bar represents the measure of the data in each category. Bars can represent frequencies, relative frequencies (proportion), or percentages.\r\n\r\n\"The\"The\r\n

Interpreting bar graphs<\/h3>\r\nAt this point, students will be presented with two datasets. They will be able to choose which one they would like to use to answer example questions before creating bar graphs using the data analysis tool.<\/span>\r\n\r\nThe bar graph below displays the number of cones each of a small ice cream shop sold on the 4th of July. Note that the counts (numbers of cones) are listed on the vertical axis while each flavor sold is listed along the horizontal axis. Examine the graph, then answer the questions in the Example that follows.\r\n\r\n\"A\r\n
\r\n

Example<\/h3>\r\nUse the Ice Cream Flavors bar graph above to answer these questions.\r\n\r\na)\u00a0 Which flavor sold the fewest number of cones?[reveal-answer q=\"901078\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"901078\"]Butter Pecan[\/hidden-answer]\r\n\r\n \r\n\r\nb) About how many cones of Neapolitan ice cream were sold?\u00a0[reveal-answer q=\"110753\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"110753\"][latex]30[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nNow that you have had a chance to become familiar with this categorical visualization, follow the directions below to use technology to create a bar graph for a real dataset.\r\n

Creating bar graphs from data<\/h3>\r\nRecall the frequency table you created earlier in this section using the Describing and Exploring Categorical Data tool.\u00a0<\/em>When you used the technology tool to create the frequency table, a bar graph was also created on that page. Let's go back to the tool to explore the bar graph. If you still have the tool open for this dataset, just follow steps 4 and 5 below to view the bar graph.\r\n
\r\n\r\nGo to the data analysis tool\u00a0 Describing and Exploring Categorical Data<\/em>\u00a0 at\u00a0 \u00a0https:\/\/dcmathpathways.shinyapps.io\/EDA_categorical\/<\/a>\r\n

Step 1) Select the\u00a0One Categorical Variable<\/strong> tab.<\/p>\r\n

Step 2)\u00a0Locate the dropdown under Enter Data<\/strong> and select From Textbook<\/strong>.<\/p>\r\n

Step 3) Locate the dropdown under Dataset<\/strong> and select Young Adults: Enjoy Music<\/strong>.<\/p>\r\nSee the bar graph under the frequency table on the tool page. You can change the appearance of the graph using the\u00a0Options\u00a0<\/strong>selections. You can show counts or percentages on the vertical axis or in the bars, change the bars from vertical to horizontal, customize order, and even change the color of the bars in the\u00a0Modify\/Include\u00a0<\/strong>section. Let's explore how to change the bars from vertical to horizontal and then change the horizontal axis from Count to Percent (%).\r\n

Step 4)\u00a0Click the Horizontal Bars<\/strong> box to change the perspective of the graph from counts as bar-heights to bar-lengths. Note how the Count range switches from the vertical axis to the horizontal axis.\u00a0<\/span><\/p>\r\n

Step 5) Click the Show Percent<\/strong> box to change the heights (or lengths of horizontal bars) from counts to percentages. Note how the Count range switches to Percent (%).\u00a0<\/span><\/p>\r\n\r\n<\/div>\r\nTake a moment to explore switching these options back and forth to see how the graph changes then answer Question 5 below.\r\n

\r\n

question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240591[\/ohm_question]\r\n\r\n[reveal-answer q=\"287570\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"287570\"]Hint: The heights of the bars represent the measure of the frequency, relative frequency, or percentage of surveyed young adults for each music rating.[\/hidden-answer]\r\n\r\n<\/div>\r\n

Pie Charts<\/h2>\r\nAnother common graph used for displaying the distribution of categorical data is a pie chart. In a pie chart<\/strong>, categories are represented by wedges in a circle and are proportional in size to the percentage of individuals\/items in each category.\u00a0There are several ways to present pie chart data visually. A pie chart may include all the information needed to read it within each wedge or they may provided some image in the chart and some in a key off to the side.\r\n\r\n\"The\"The\r\n

Interpreting pie charts<\/h3>\r\nPie charts are useful for showing percentages (parts of a whole) at some particular instance in time. For example, the following chart displays flavors of ice cream sold at an ice cream shop as a percentage of all ice cream sales on July 4th. This chart contains the same information as the bar chart does above, but shows percentages rather than counts.\r\n\r\n\"The\r\n
\r\n

Example<\/h3>\r\nUse the chart above to answer the following questions.\r\n\r\na) What flavor made up the largest percentage of ice cream sales?\r\n[reveal-answer q=\"140681\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"140681\"]Mint Chocolate Chip[\/hidden-answer]\r\n\r\nb) What percent of sales was attributed to strawberry ice cream?\r\n

[reveal-answer q=\"806070\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"806070\"][latex]18[\/latex]%[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n

Creating pie charts from data<\/h3>\r\nWhen you used the Describing and Exploring Categorical Data\u00a0<\/em>data tool to create the frequency table and bar graph, you also had the option to create a pie chart. Let's do that now. If you still have the tool open, skip to Step 4 below.\r\n
\r\n\r\nGo to the data analysis tool\u00a0 Describing and Exploring Categorical Data<\/em>\u00a0 at\u00a0 \u00a0https:\/\/dcmathpathways.shinyapps.io\/EDA_categorical\/<\/a>\r\n

Step 1) Select the\u00a0One Categorical Variable<\/strong> tab.<\/p>\r\n

Step 2)\u00a0Locate the dropdown under Enter Data<\/strong> and select From Textbook<\/strong>.<\/p>\r\n

Step 3) Locate the dropdown under Dataset<\/strong> and select Young Adults: Enjoy Music<\/strong>.<\/p>\r\n

Step 4)\u00a0Under the\u00a0Additional Plots<\/strong> section, select Pie Chart<\/strong>.\u00a0<\/span>Scroll down to see the pie chart on the page under the bar graph.<\/p>\r\n\r\n<\/div>\r\n

\r\n

question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240593[\/ohm_question]\r\n\r\n[reveal-answer q=\"282030\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"282030\"]Make sure that One Categorical Variable and the correct dataset (Young Adults: Enjoy Music) are selected.[\/hidden-answer]\r\n\r\n<\/div>\r\nIt's difficult to visualize a summary of the Enjoy music <\/em>categories since just one or two of them dominate the chart. Let's leave the tool now and explore another one of the variables from the dataset: Punctuality<\/em>. The following pie chart displays the distribution of the categorical variable Punctuality<\/em>. Use this pie chart to answer Questions 7 and 8 below.\r\n\r\n\"A\r\n
\r\n

question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]240757[\/ohm_question]\r\n\r\n[reveal-answer q=\"100546\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"100546\"]Refer to the key next to the chart.[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 8<\/h3>\r\n[ohm_question hide_question_numbers=1]240758[\/ohm_question]\r\n\r\n[reveal-answer q=\"899480\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"899480\"]What do you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>","rendered":"

Bar Graphs<\/h2>\n

One of the most commonly used graphs for visualizing the distribution of a categorical variable is a bar graph. In a bar graph<\/strong>, categories are represented by bars that are separated from each other. The bars can be vertical or horizontal, and the height (or length) of each bar represents the measure of the data in each category. Bars can represent frequencies, relative frequencies (proportion), or percentages.<\/p>\n

\"The\"The<\/p>\n

Interpreting bar graphs<\/h3>\n

At this point, students will be presented with two datasets. They will be able to choose which one they would like to use to answer example questions before creating bar graphs using the data analysis tool.<\/span><\/p>\n

The bar graph below displays the number of cones each of a small ice cream shop sold on the 4th of July. Note that the counts (numbers of cones) are listed on the vertical axis while each flavor sold is listed along the horizontal axis. Examine the graph, then answer the questions in the Example that follows.<\/p>\n

\"A<\/p>\n

\n

Example<\/h3>\n

Use the Ice Cream Flavors bar graph above to answer these questions.<\/p>\n

a)\u00a0 Which flavor sold the fewest number of cones?<\/p>\n

Show Solution<\/span><\/p>\n
Butter Pecan<\/div>\n<\/div>\n

 <\/p>\n

b) About how many cones of Neapolitan ice cream were sold?\u00a0<\/p>\n

Show Solution<\/span><\/p>\n
[latex]30[\/latex]<\/div>\n<\/div>\n<\/div>\n

Now that you have had a chance to become familiar with this categorical visualization, follow the directions below to use technology to create a bar graph for a real dataset.<\/p>\n

Creating bar graphs from data<\/h3>\n

Recall the frequency table you created earlier in this section using the Describing and Exploring Categorical Data tool.\u00a0<\/em>When you used the technology tool to create the frequency table, a bar graph was also created on that page. Let’s go back to the tool to explore the bar graph. If you still have the tool open for this dataset, just follow steps 4 and 5 below to view the bar graph.<\/p>\n

\n

Go to the data analysis tool\u00a0 Describing and Exploring Categorical Data<\/em>\u00a0 at\u00a0 \u00a0https:\/\/dcmathpathways.shinyapps.io\/EDA_categorical\/<\/a><\/p>\n

Step 1) Select the\u00a0One Categorical Variable<\/strong> tab.<\/p>\n

Step 2)\u00a0Locate the dropdown under Enter Data<\/strong> and select From Textbook<\/strong>.<\/p>\n

Step 3) Locate the dropdown under Dataset<\/strong> and select Young Adults: Enjoy Music<\/strong>.<\/p>\n

See the bar graph under the frequency table on the tool page. You can change the appearance of the graph using the\u00a0Options\u00a0<\/strong>selections. You can show counts or percentages on the vertical axis or in the bars, change the bars from vertical to horizontal, customize order, and even change the color of the bars in the\u00a0Modify\/Include\u00a0<\/strong>section. Let’s explore how to change the bars from vertical to horizontal and then change the horizontal axis from Count to Percent (%).<\/p>\n

Step 4)\u00a0Click the Horizontal Bars<\/strong> box to change the perspective of the graph from counts as bar-heights to bar-lengths. Note how the Count range switches from the vertical axis to the horizontal axis.\u00a0<\/span><\/p>\n

Step 5) Click the Show Percent<\/strong> box to change the heights (or lengths of horizontal bars) from counts to percentages. Note how the Count range switches to Percent (%).\u00a0<\/span><\/p>\n<\/div>\n

Take a moment to explore switching these options back and forth to see how the graph changes then answer Question 5 below.<\/p>\n

\n

question 5<\/h3>\n