{"id":421,"date":"2022-07-11T16:33:29","date_gmt":"2022-07-11T16:33:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=421"},"modified":"2022-07-11T16:54:05","modified_gmt":"2022-07-11T16:54:05","slug":"calculating-the-mean-and-median-of-a-data-set-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/calculating-the-mean-and-median-of-a-data-set-background-youll-need-2\/","title":{"raw":"Calculating the Mean and Median of a Data Set: Background You'll Need 2","rendered":"Calculating the Mean and Median of a Data Set: Background You’ll Need 2"},"content":{"raw":"

Illustrating Frequency with Histograms<\/h2>\r\nBelow we are given a histogram for the variable Hours of Sleep Per Night (Weekend)<\/em>. Recall that a histogram displays the distribution of a quantitative variable but, unlike the dotplot in which each observation is stacked above each value appearing, a histogram gathers groups of observations up into its bars.\r\n
\r\n

recall<\/h3>\r\nYou may wish to refresh your understanding of how data is represented in a histogram.\r\n\r\nCore skill: [reveal-answer q=\"819814\"]Understand the features of a histogram[\/reveal-answer]\r\n[hidden-answer a=\"819814\"]A histogram is a graph for displaying the distribution of a quantitative variable in which the frequency of an interval of values is represented by the height of a rectangular bar that summarizes a group of observations over an interval of values. The width, called binwidth<\/em>, of each bar is equivalent and can represent any interval of values desired.\u00a0[\/hidden-answer]\r\n\r\n<\/div>\r\nUse the following histogram to address Questions 4-7.\r\n\r\n\"A\r\n\r\nAs you did with for the dotplot above, first orient yourself to the information conveyed in the histogram by answering Question 4.\u00a0 Then, compare and contrast the histogram to the dotplot in Question 5. Finally, read and interpret the histogram to answer Questions 6 and 7.\r\n
\r\n

question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]240947[\/ohm_question]\r\n\r\n[reveal-answer q=\"941946\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"941946\"]See the recall box above for a description of the features of a histogram.[\/hidden-answer]\r\n\r\n<\/div>\r\nNow that you are familiar with the information presented in the histogram, look back at the dotplot and consider general differences and similarities in the two types of displays.\r\n
\r\n

question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240948[\/ohm_question]\r\n\r\n[reveal-answer q=\"207574\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"207574\"]What do you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nHistograms are more commonly encountered than dotplots as a visualization of quantitative data since they can more concisely display large data sets. Dotplots are more appropriate for smaller sets of data in which the observations (the dots) are not overwhelmingly numerous.\r\n\r\nNow use the histogram to answer questions about the variable\u00a0Hours of Sleep Per Night (Weekend)<\/em>.\r\n
\r\n

question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240951[\/ohm_question]\r\n\r\n[reveal-answer q=\"350070\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"350070\"]The height of each bar represents the observations grouped within the bar.[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]240952[\/ohm_question]\r\n\r\n[reveal-answer q=\"107203\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"107203\"]What do you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nLet's examine the distribution of a variable from another data set.\r\n\r\nThe histogram below displays the frequency of sodium content per serving for\u00a0[latex]20[\/latex] different varieties of cereals.[footnote] Agresti, A., Franklin, C. A., & Klingenberg, B. (2021). Statistics: The art and science of learning from data, 5th edition. Pearson. https:\/\/www.pearson.com\/us\/higher-education\/program\/Agresti-My-Lab-Statistics-with-Pearson-e-Text-Access-Card-for-Statistics-The-Art-and-Science-of-Learning-from-Data-18-Weeks-5th-Edition\/PGM2788191.html [\/footnote]\r\n\r\n\"A\r\n
\r\n

question 8<\/h3>\r\n[ohm_question hide_question_numbers=1]240955[\/ohm_question]\r\n\r\n[reveal-answer q=\"357681\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"357681\"]Count all the bars that represent sodium of at least\u00a0[latex]200[\/latex] mg.[\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 9<\/h3>\r\n[ohm_question hide_question_numbers=1]240957[\/ohm_question]\r\n\r\n[reveal-answer q=\"779992\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"779992\"]Count all the bars that represent sodium less than [latex]200[\/latex] mg.[\/hidden-answer]\r\n\r\n<\/div>","rendered":"

Illustrating Frequency with Histograms<\/h2>\n

Below we are given a histogram for the variable Hours of Sleep Per Night (Weekend)<\/em>. Recall that a histogram displays the distribution of a quantitative variable but, unlike the dotplot in which each observation is stacked above each value appearing, a histogram gathers groups of observations up into its bars.<\/p>\n

\n

recall<\/h3>\n

You may wish to refresh your understanding of how data is represented in a histogram.<\/p>\n

Core skill: <\/p>\n

Understand the features of a histogram<\/span><\/p>\n
A histogram is a graph for displaying the distribution of a quantitative variable in which the frequency of an interval of values is represented by the height of a rectangular bar that summarizes a group of observations over an interval of values. The width, called binwidth<\/em>, of each bar is equivalent and can represent any interval of values desired.\u00a0<\/div>\n<\/div>\n<\/div>\n

Use the following histogram to address Questions 4-7.<\/p>\n

\"A<\/p>\n

As you did with for the dotplot above, first orient yourself to the information conveyed in the histogram by answering Question 4.\u00a0 Then, compare and contrast the histogram to the dotplot in Question 5. Finally, read and interpret the histogram to answer Questions 6 and 7.<\/p>\n

\n

question 4<\/h3>\n