{"id":28,"date":"2022-05-20T16:59:03","date_gmt":"2022-05-20T16:59:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-variability-of-data-sets-corequisite-support-activity-continued\/"},"modified":"2022-07-11T18:36:15","modified_gmt":"2022-07-11T18:36:15","slug":"comparing-variability-of-data-sets-corequisite-support-activity-continued","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-variability-of-data-sets-corequisite-support-activity-continued\/","title":{"raw":"Comparing Variability of Data Sets: Background You'll Need 2","rendered":"Comparing Variability of Data Sets: Background You’ll Need 2"},"content":{"raw":"

Sample size and mean<\/h2>\r\n
\r\n\r\nGo to the Describing and Exploring Quantitative Variables tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.\r\n

Step 1) Select the Single Group<\/strong> tab.<\/p>\r\n

Step 2) Locate the drop-down menu under Enter Data<\/strong> and select From Textbook<\/strong>.<\/p>\r\n

Step 3) Locate the drop-down menu under Data Set<\/strong> and select Hurricane Damage<\/strong>.<\/p>\r\n\r\n<\/div>\r\nIn the descriptive statistics at the top of the applet, you will see the sample size [latex]\\left(n\\right)[\/latex] and the mean [latex]\\left(\\bar{x}\\right)[\/latex] of the data set.\r\n

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question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]241044[\/ohm_question]\r\n\r\n[reveal-answer q=\"943053\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"943053\"]Make sure the Data Set \"Hurricane Damage\" is selected then locate the Sample Size in Descriptive Statistics.[\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]241045[\/ohm_question]\r\n\r\n[reveal-answer q=\"77790\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"77790\"]What is the name of the variable of interest? Use units when expressing your answer to put it in context.[\/hidden-answer]\r\n\r\n<\/div>\r\nOn the next page, you will continue to learn more about deviation from the mean.\r\n

Deviation from the mean<\/h2>\r\nA deviation from the mean<\/strong> is the distance between an observation, [latex]x[\/latex], in a data set and the mean, [latex]\\bar{x}[\/latex], of the data set. To calculate the deviation from the mean, subtract the sample mean from each observation in the data set [latex]\\left(x-\\bar{x}\\right)[\/latex].\r\n\r\nPractice calculating the deviation from the mean in the following interactive example. Then, for the data table that follows, calculate the deviation from the mean to answer Question 4.\r\n
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Example<\/h3>\r\nSeven of\u00a0[latex]50[\/latex] observations a student made about her commute time by bicycle from her apartment to school are listed in the following table. Her mean commute time was\u00a0[latex]10[\/latex] minutes,\u00a0[latex]\\bar{x}=10[\/latex]. Use this information to calculate the deviation from the mean [latex]\\left(x-\\bar{x}\\right)[\/latex] for each of the seven observations given.\r\n\r\nExample: See the first entry in the table: an observed 8 minute commute time.\u00a0 Given a mean commute time of 10 minutes, the deviation from the mean for the observation of 8 minutes is [latex]8-10=-2[\/latex].\r\n\r\nComplete the table then check your answers below.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
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Bike Ride to School (in minutes)<\/strong><\/p>\r\n

[latex]x[\/latex]<\/strong><\/p>\r\n<\/td>\r\n

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Deviation from the Mean (in minutes)<\/strong><\/p>\r\n

[latex]x-\\bar{x}[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n

8<\/strong><\/td>\r\n[latex]8 - 10 = -2[\/latex]<\/td>\r\n<\/tr>\r\n
10<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
12<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
14<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
5<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
15<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
9<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"129517\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"129517\"]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\r\n

Bike Ride to School (in minutes)<\/strong><\/p>\r\n

[latex]x[\/latex]<\/strong><\/p>\r\n<\/td>\r\n

\r\n

Deviation from the Mean (in minutes)<\/strong><\/p>\r\n

[latex]x-\\bar{x}[\/latex]<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n

8<\/strong><\/td>\r\n[latex]8 - 10 = -2[\/latex]<\/td>\r\n<\/tr>\r\n
10<\/strong><\/td>\r\n[latex]10 - 10 = 0[\/latex]<\/td>\r\n<\/tr>\r\n
12<\/strong><\/td>\r\n[latex]12 - 10 = 2[\/latex]<\/td>\r\n<\/tr>\r\n
14<\/strong><\/td>\r\n[latex]14 - 10 = 4[\/latex]<\/td>\r\n<\/tr>\r\n
5<\/strong><\/td>\r\n[latex]5 - 10 = -5[\/latex]<\/td>\r\n<\/tr>\r\n
15<\/strong><\/td>\r\n[latex]15 - 10 = 5[\/latex]<\/td>\r\n<\/tr>\r\n
9<\/strong><\/td>\r\n[latex]9 - 10 = -1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nEach value listed in the first column is identified as an observation. Subtract the given mean, [latex]\\bar{x}=10[\/latex] from each observation to obtain the deviation from the mean. For example, the observation of\u00a0[latex]12[\/latex] minutes results in that ride to school being\u00a0[latex]2[\/latex] minutes above the mean (or a longer ride), while the observation of\u00a0[latex]5[\/latex] results in that ride to school being\u00a0[latex]5[\/latex] minutes below the mean (or a shorter ride).\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow it's your turn to calculate the deviation from the mean for ten of the 30 hurricane damage observations from the data set \"Hurricane Damage.\" Follow the instructions above to reopen the data set if you have closed it.\r\n
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question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]241046[\/ohm_question]\r\n
\r\n\r\n[reveal-answer q=\"719277\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"719277\"]Locate the value for [latex]\\bar{x}[\/latex] in Descriptive Statistics.[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>","rendered":"

Sample size and mean<\/h2>\n
\n

Go to the Describing and Exploring Quantitative Variables tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.<\/p>\n

Step 1) Select the Single Group<\/strong> tab.<\/p>\n

Step 2) Locate the drop-down menu under Enter Data<\/strong> and select From Textbook<\/strong>.<\/p>\n

Step 3) Locate the drop-down menu under Data Set<\/strong> and select Hurricane Damage<\/strong>.<\/p>\n<\/div>\n

In the descriptive statistics at the top of the applet, you will see the sample size [latex]\\left(n\\right)[\/latex] and the mean [latex]\\left(\\bar{x}\\right)[\/latex] of the data set.<\/p>\n

\n

question 2<\/h3>\n