{"id":468,"date":"2022-07-11T18:39:52","date_gmt":"2022-07-11T18:39:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=468"},"modified":"2022-08-09T20:02:18","modified_gmt":"2022-08-09T20:02:18","slug":"interpreting-the-mean-and-median-of-a-data-set-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/interpreting-the-mean-and-median-of-a-data-set-background-youll-need-2\/","title":{"raw":"Interpreting the Mean and Median of a Data Set: Background You'll Need 2","rendered":"Interpreting the Mean and Median of a Data Set: Background You’ll Need 2"},"content":{"raw":"

\u00a0Calculating Mean<\/h2>\r\n
\r\n

Recall<\/h3>\r\nDo you recall how to calculate the mean of a data set?\r\n\r\n[reveal-answer q=\"330489\"]Core Skill: Calculating a Mean[\/reveal-answer]\r\n[hidden-answer a=\"330489\"]\r\n\r\nThe formula to calculate the mean is [latex]\\bar{x}=\\dfrac{\\sum{x}}{n}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Employee<\/strong><\/td>\r\n\r\n

Monthly Salary in January<\/strong><\/p>\r\n

(in thousands of dollars)<\/strong><\/p>\r\n<\/td>\r\n

\r\n

Monthly Salary in February<\/strong><\/p>\r\n

(in thousands of dollars)<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n

Employee 1<\/strong><\/td>\r\n[latex]4[\/latex]<\/td>\r\n[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n
Employee 2<\/strong><\/td>\r\n[latex]6[\/latex]<\/td>\r\n[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n
Employee 3<\/strong><\/td>\r\n[latex]3[\/latex]<\/td>\r\n[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n
Employee 4<\/strong><\/td>\r\n[latex]5[\/latex]<\/td>\r\n[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n
Employee 5<\/strong><\/td>\r\n[latex]6[\/latex]<\/td>\r\n[latex]6[\/latex]<\/td>\r\n<\/tr>\r\n
Employee 6<\/strong><\/td>\r\n[latex]3[\/latex]<\/td>\r\n[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n

question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]241073[\/ohm_question]\r\n\r\n[reveal-answer q=\"50836\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"50836\"]Recall the process for finding the mean. See the Recall box at the top of this page or refer to Calculating Mean and Median: What to Know<\/em>.[\/hidden-answer]\r\n\r\n<\/div>\r\nThe same steps we used to calculate the median with the statistics tool can be used to find the mean. Use the tool to find the mean of the January salaries and compare it to your by hand calculation. Did they match?\r\n\r\nGo to the Describing and Exploring Quantitative Variables tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a> and confirm your answer using the online tool.\r\n
\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 Your Own<\/strong>.<\/p>\r\n

Step 3) Under\u00a0Do you have,\u00a0<\/strong>select\u00a0Individual Observations<\/strong>.<\/p>\r\n

Step 4) Under Name of Variable<\/strong>, type \"January Salaries (in thousands $)\".<\/p>\r\n

Step 5) Under Enter observations<\/strong>, enter the data list, separated by spaces: \u201c4 6 3 5 6 3.\u201d The median will be among the Descriptive Statistics listed in the tool.<\/p>\r\n\r\n<\/div>\r\n

\r\n

question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]241076[\/ohm_question]\r\n\r\n[reveal-answer q=\"180400\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"180400\"]The mean will be among the Descriptive Statistics listed in the tool[\/hidden-answer]\r\n\r\n<\/div>\r\nNow, consider what the mean tells us about the data. See the recall box at the top of the page for a hint.\r\n
\r\n

question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]241078[\/ohm_question]\r\n\r\n[reveal-answer q=\"129961\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"129961\"]Consider what it means for a value to be an \"average\" value for the data set.[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]241084[\/ohm_question]\r\n\r\n[reveal-answer q=\"68470\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"68470\"]What do you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n","rendered":"

\u00a0Calculating Mean<\/h2>\n
\n

Recall<\/h3>\n

Do you recall how to calculate the mean of a data set?<\/p>\n

Core Skill: Calculating a Mean<\/span><\/p>\n
\n

The formula to calculate the mean is [latex]\\bar{x}=\\dfrac{\\sum{x}}{n}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n\n\n\n\n\n\n
Employee<\/strong><\/td>\n\n

Monthly Salary in January<\/strong><\/p>\n

(in thousands of dollars)<\/strong><\/p>\n<\/td>\n

\n

Monthly Salary in February<\/strong><\/p>\n

(in thousands of dollars)<\/strong><\/p>\n<\/td>\n<\/tr>\n

Employee 1<\/strong><\/td>\n[latex]4[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n<\/tr>\n
Employee 2<\/strong><\/td>\n[latex]6[\/latex]<\/td>\n[latex]8[\/latex]<\/td>\n<\/tr>\n
Employee 3<\/strong><\/td>\n[latex]3[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n<\/tr>\n
Employee 4<\/strong><\/td>\n[latex]5[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n<\/tr>\n
Employee 5<\/strong><\/td>\n[latex]6[\/latex]<\/td>\n[latex]6[\/latex]<\/td>\n<\/tr>\n
Employee 6<\/strong><\/td>\n[latex]3[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

question 4<\/h3>\n