{"id":1219,"date":"2022-04-07T22:37:02","date_gmt":"2022-04-07T22:37:02","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&p=1219"},"modified":"2022-05-20T16:44:46","modified_gmt":"2022-05-20T16:44:46","slug":"comparing-variability-of-data-sets-what-to-know-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/comparing-variability-of-data-sets-what-to-know-3\/","title":{"raw":"Comparing Variability of Data Sets: What to Know 3","rendered":"Comparing Variability of Data Sets: What to Know 3"},"content":{"raw":"

Using Technology to Obtain Descriptive Statistics<\/h2>\r\nLet's go to the technology now and recall how to load a data set in order to describe and explore it.\r\n\r\nFor Questions 4 and 5, recall the sleep study in which you investigated whether college students' chronotypes tend to be larks (morning people) or owls (night people) by examining graphical representations of the data. Let's use the data set from that study again here.\r\n
\r\n\r\nGo to the Describing and Exploring Quantitative Variables<\/em> 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 Sleep Study: Average Sleep<\/strong>.<\/p>\r\n\r\n<\/div>\r\n

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question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]241058[\/ohm_question]\r\n\r\n[reveal-answer q=\"559868\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"559868\"]If a data set represents an entire population, there are probably not many good unanswered statistical questions about the population. What would you consider to be the population for the Sleep Study? [\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]241059[\/ohm_question]\r\n\r\n[reveal-answer q=\"341628\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"341628\"]Obtain measures of center from \"Descriptive Statistics.\"[\/hidden-answer]\r\n\r\n<\/div>\r\n

Measures of Variability<\/h2>\r\nIn statistics, we are particularly interested in understanding how data are distributed and where each observation is in reference to the mean. How spread out a set of observations are is called variability<\/strong> (also called spread or dispersion). In the remainder of this section, we will focus on three measures of spread: standard deviation, variance, and range.\r\n
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Recall<\/h3>\r\nWe'll be using statistical formulas and symbols to discuss measures of variability. Take a moment to recall the formula you learned to calculate the mean of a sample. What symbols do we use to represent sample mean, summation, and sample size?\r\n\r\nCore skill: [reveal-answer q=\"450894\"]Express the formula for calculating the mean of a sample[\/reveal-answer]\r\n[hidden-answer a=\"450894\"]\r\n\r\n[latex]\\bar{x}=\\dfrac{\\sum{x}}{n}[\/latex] where [latex]\\bar{x}[\/latex] denotes the sample mean, [latex]\\sum{x}[\/latex] indicates to take a sum of all the sample values [latex]x[\/latex],\u00a0and [latex]n[\/latex] indicates the sample size.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nContinue to the next page to take a deeper dive into the different measures of variability (spread), beginning with standard deviation.","rendered":"

Using Technology to Obtain Descriptive Statistics<\/h2>\n

Let’s go to the technology now and recall how to load a data set in order to describe and explore it.<\/p>\n

For Questions 4 and 5, recall the sleep study in which you investigated whether college students’ chronotypes tend to be larks (morning people) or owls (night people) by examining graphical representations of the data. Let’s use the data set from that study again here.<\/p>\n

\n

Go to the Describing and Exploring Quantitative Variables<\/em> 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 Sleep Study: Average Sleep<\/strong>.<\/p>\n<\/div>\n

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question 4<\/h3>\n