{"id":481,"date":"2022-07-11T18:48:04","date_gmt":"2022-07-11T18:48:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=481"},"modified":"2022-08-08T17:26:24","modified_gmt":"2022-08-08T17:26:24","slug":"interpreting-the-mean-and-median-of-a-data-set-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/interpreting-the-mean-and-median-of-a-data-set-learn-it-2\/","title":{"raw":"Interpreting the Mean and Median of a Data Set: Learn It 2","rendered":"Interpreting the Mean and Median of a Data Set: Learn It 2"},"content":{"raw":"

Mean and Median<\/h3>\r\nFriends<\/em> was a popular American television show that aired from 1994 to 2004. The show followed a group of six friends living in New York City and chronicled their relationships and day-to-day adventures. The show became known in popular culture for its comedy and for the closeness of its cast.[footnote]Encyclopedia Britannica. (n.d.). Friends. In Encyclopedia Britannica.com<\/em>. https:\/\/www.britannica.com\/topic\/Friends[\/footnote]\r\n\r\nThe following table lists the number of U.S. viewers of each episode of the\u00a0[latex]10[\/latex]th<\/sup> and final season of Friends.[footnote]Mock, T. (2020). A weekly data project aimed at the R ecosystem<\/em>. TidyTuesday. https:\/\/github.com\/rfordatascience\/tidytuesday\/blob\/master\/data\/2020\/2020-09-08\/readme.md#friends_infocsv[\/footnote]\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Friends Final Season Viewers by episode<\/span>\r\n<\/strong><\/caption>\r\n
Episode Number<\/strong><\/td>\r\nEpisode Title<\/strong><\/td>\r\nAir Date<\/strong><\/td>\r\nU.S. Viewers (Millions)<\/strong><\/td>\r\n<\/tr>\r\n
1<\/strong><\/td>\r\nThe One After Joey and Rachel Kiss<\/td>\r\n9\/25\/03<\/td>\r\n[latex]24.54[\/latex]<\/td>\r\n<\/tr>\r\n
2<\/strong><\/td>\r\nThe One Where Ross Is Fine<\/td>\r\n10\/2\/03<\/td>\r\n[latex]22.38[\/latex]<\/td>\r\n<\/tr>\r\n
3<\/strong><\/td>\r\nThe One with Ross's Tan<\/td>\r\n10\/9\/03<\/td>\r\n[latex]21.87[\/latex]<\/td>\r\n<\/tr>\r\n
4<\/strong><\/td>\r\nThe One with the Cake<\/td>\r\n10\/23\/03<\/td>\r\n[latex]18.77[\/latex]<\/td>\r\n<\/tr>\r\n
5<\/strong><\/td>\r\nThe One Where Rachel's Sister Babysits<\/td>\r\n10\/30\/03<\/td>\r\n[latex]19.37[\/latex]<\/td>\r\n<\/tr>\r\n
6<\/strong><\/td>\r\nThe One with Ross's Grant<\/td>\r\n11\/6\/03<\/td>\r\n[latex]20.38[\/latex]<\/td>\r\n<\/tr>\r\n
7<\/strong><\/td>\r\nThe One with the Home Study<\/td>\r\n11\/13\/03<\/td>\r\n[latex]20.21[\/latex]<\/td>\r\n<\/tr>\r\n
8<\/strong><\/td>\r\nThe One with the Late Thanksgiving<\/td>\r\n11\/20\/03<\/td>\r\n[latex]20.66[\/latex]<\/td>\r\n<\/tr>\r\n
9<\/strong><\/td>\r\nThe One with the Birth Mother<\/td>\r\n1\/8\/04<\/td>\r\n[latex]25.49[\/latex]<\/td>\r\n<\/tr>\r\n
10<\/strong><\/td>\r\nThe One Where Chandler Gets Caught<\/td>\r\n1\/15\/04<\/td>\r\n[latex]26.68[\/latex]<\/td>\r\n<\/tr>\r\n
11<\/strong><\/td>\r\nThe One Where the Stripper Cries<\/td>\r\n2\/5\/04<\/td>\r\n[latex]24.91[\/latex]<\/td>\r\n<\/tr>\r\n
12<\/strong><\/td>\r\nThe One with Phoebe's Wedding<\/td>\r\n2\/12\/04<\/td>\r\n[latex]25.9[\/latex]<\/td>\r\n<\/tr>\r\n
13<\/strong><\/td>\r\nThe One Where Joey Speaks French<\/td>\r\n2\/19\/04<\/td>\r\n[latex]24.27[\/latex]<\/td>\r\n<\/tr>\r\n
14<\/strong><\/td>\r\nThe One with Princess Consuela<\/td>\r\n2\/26\/04<\/td>\r\n[latex]22.83[\/latex]<\/td>\r\n<\/tr>\r\n
15<\/strong><\/td>\r\nThe One Where Estelle Dies<\/td>\r\n4\/22\/04<\/td>\r\n[latex]22.64[\/latex]<\/td>\r\n<\/tr>\r\n
16<\/strong><\/td>\r\nThe One with Rachel's Going Away Party<\/td>\r\n4\/29\/04<\/td>\r\n[latex]24.51[\/latex]<\/td>\r\n<\/tr>\r\n
17<\/strong><\/td>\r\nThe Last One*<\/td>\r\n5\/6\/04<\/td>\r\n[latex]52.46[\/latex]<\/td>\r\n<\/tr>\r\n
18<\/strong><\/td>\r\nThe Last One*<\/td>\r\n5\/6\/04<\/td>\r\n[latex]52.46[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/thead>\r\n<\/table>\r\nWe'll use technology to analyze this data set.<\/span>\r\n\r\n<\/div>\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 Your Own<\/strong>.<\/p>\r\n

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

Step 4)\u00a0Under Name of Variable<\/strong>, type \u201cU.S. Viewers (Millions).\u201d<\/p>\r\n

Step 5) Cut and paste or enter the data presented in the above table for U.S. Viewers (Millions).<\/p>\r\n\r\n<\/div>\r\n

In the following questions, you'll need to interpret the mean and median of the data set. Recall that we think of the mean as the \"average\" data value and the median as the 50th percentile, the value that splits the data in half.\u00a0If needed, you may return to\u00a0Calculating the Mean and Median of a Data Set: What to Know<\/em><\/a> for a refresher of these interpretations of mean and median.<\/p>\r\n\r\nUse the data set for the TV show\u00a0Friends<\/em> to answer the questions below.\r\n

\r\n

question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]241087[\/ohm_question]\r\n\r\n[reveal-answer q=\"253029\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"253029\"]The median will be located in Descriptive Statistics.[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]241088[\/ohm_question]\r\n\r\n[reveal-answer q=\"497957\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"497957\"]The median is the\u00a0[latex]50[\/latex]th<\/sup> percentile and splits the data in half.[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]241089[\/ohm_question]\r\n\r\n[reveal-answer q=\"704874\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"704874\"]The mean will be located in Descriptive Statistics[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]241090[\/ohm_question]\r\n\r\n[reveal-answer q=\"203004\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"203004\"]The mean is what we think of as the \"average\" value in the set.[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]241092[\/ohm_question]\r\n\r\n[reveal-answer q=\"412918\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"412918\"]Use Descriptive Statistics in the tool to compare them.[\/hidden-answer]\r\n\r\n<\/div>","rendered":"

Mean and Median<\/h3>\n

Friends<\/em> was a popular American television show that aired from 1994 to 2004. The show followed a group of six friends living in New York City and chronicled their relationships and day-to-day adventures. The show became known in popular culture for its comedy and for the closeness of its cast.[1]<\/sup><\/a><\/p>\n

The following table lists the number of U.S. viewers of each episode of the\u00a0[latex]10[\/latex]th<\/sup> and final season of Friends.[2]<\/sup><\/a><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*Note: the final two episodes aired back-to-back on the same night\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/caption>\r\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Friends Final Season Viewers by episode<\/span>
\n<\/strong><\/caption>\n
Episode Number<\/strong><\/td>\nEpisode Title<\/strong><\/td>\nAir Date<\/strong><\/td>\nU.S. Viewers (Millions)<\/strong><\/td>\n<\/tr>\n
1<\/strong><\/td>\nThe One After Joey and Rachel Kiss<\/td>\n9\/25\/03<\/td>\n[latex]24.54[\/latex]<\/td>\n<\/tr>\n
2<\/strong><\/td>\nThe One Where Ross Is Fine<\/td>\n10\/2\/03<\/td>\n[latex]22.38[\/latex]<\/td>\n<\/tr>\n
3<\/strong><\/td>\nThe One with Ross’s Tan<\/td>\n10\/9\/03<\/td>\n[latex]21.87[\/latex]<\/td>\n<\/tr>\n
4<\/strong><\/td>\nThe One with the Cake<\/td>\n10\/23\/03<\/td>\n[latex]18.77[\/latex]<\/td>\n<\/tr>\n
5<\/strong><\/td>\nThe One Where Rachel’s Sister Babysits<\/td>\n10\/30\/03<\/td>\n[latex]19.37[\/latex]<\/td>\n<\/tr>\n
6<\/strong><\/td>\nThe One with Ross’s Grant<\/td>\n11\/6\/03<\/td>\n[latex]20.38[\/latex]<\/td>\n<\/tr>\n
7<\/strong><\/td>\nThe One with the Home Study<\/td>\n11\/13\/03<\/td>\n[latex]20.21[\/latex]<\/td>\n<\/tr>\n
8<\/strong><\/td>\nThe One with the Late Thanksgiving<\/td>\n11\/20\/03<\/td>\n[latex]20.66[\/latex]<\/td>\n<\/tr>\n
9<\/strong><\/td>\nThe One with the Birth Mother<\/td>\n1\/8\/04<\/td>\n[latex]25.49[\/latex]<\/td>\n<\/tr>\n
10<\/strong><\/td>\nThe One Where Chandler Gets Caught<\/td>\n1\/15\/04<\/td>\n[latex]26.68[\/latex]<\/td>\n<\/tr>\n
11<\/strong><\/td>\nThe One Where the Stripper Cries<\/td>\n2\/5\/04<\/td>\n[latex]24.91[\/latex]<\/td>\n<\/tr>\n
12<\/strong><\/td>\nThe One with Phoebe’s Wedding<\/td>\n2\/12\/04<\/td>\n[latex]25.9[\/latex]<\/td>\n<\/tr>\n
13<\/strong><\/td>\nThe One Where Joey Speaks French<\/td>\n2\/19\/04<\/td>\n[latex]24.27[\/latex]<\/td>\n<\/tr>\n
14<\/strong><\/td>\nThe One with Princess Consuela<\/td>\n2\/26\/04<\/td>\n[latex]22.83[\/latex]<\/td>\n<\/tr>\n
15<\/strong><\/td>\nThe One Where Estelle Dies<\/td>\n4\/22\/04<\/td>\n[latex]22.64[\/latex]<\/td>\n<\/tr>\n
16<\/strong><\/td>\nThe One with Rachel’s Going Away Party<\/td>\n4\/29\/04<\/td>\n[latex]24.51[\/latex]<\/td>\n<\/tr>\n
17<\/strong><\/td>\nThe Last One*<\/td>\n5\/6\/04<\/td>\n[latex]52.46[\/latex]<\/td>\n<\/tr>\n
18<\/strong><\/td>\nThe Last One*<\/td>\n5\/6\/04<\/td>\n[latex]52.46[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/thead>\n<\/table>\n

We’ll use technology to analyze this data set.<\/span><\/p>\n<\/div>\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 Your Own<\/strong>.<\/p>\n

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

Step 4)\u00a0Under Name of Variable<\/strong>, type \u201cU.S. Viewers (Millions).\u201d<\/p>\n

Step 5) Cut and paste or enter the data presented in the above table for U.S. Viewers (Millions).<\/p>\n<\/div>\n

In the following questions, you’ll need to interpret the mean and median of the data set. Recall that we think of the mean as the “average” data value and the median as the 50th percentile, the value that splits the data in half.\u00a0If needed, you may return to\u00a0Calculating the Mean and Median of a Data Set: What to Know<\/em><\/a> for a refresher of these interpretations of mean and median.<\/p>\n

Use the data set for the TV show\u00a0Friends<\/em> to answer the questions below.<\/p>\n

\n

question 1<\/h3>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*Note: the final two episodes aired back-to-back on the same night\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/caption>\n