{"id":492,"date":"2021-12-20T14:50:04","date_gmt":"2021-12-20T14:50:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=492"},"modified":"2022-02-17T20:13:46","modified_gmt":"2022-02-17T20:13:46","slug":"corequisite-support-activity-4e","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/corequisite-support-activity-4e\/","title":{"raw":"Corequisite Support Activity for Z-Score and the Empirical Rule: 4E - 28","rendered":"Corequisite Support Activity for Z-Score and the Empirical Rule: 4E &#8211; 28"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>What you'll need to know<\/h3>\r\nIn this support activity you'll become familiar with the following:\r\n<ul>\r\n \t<li><a href=\"#InterpretStdDevUnits\">Calculate and interpret units of standard deviation as a measure of distance.<\/a><\/li>\r\n \t<li><a href=\"#CalcDistStdDev\">Calculate the distance in units of standard deviations of an observed value from the population mean.<\/a><\/li>\r\n \t<li><a href=\"#IdentMistakes\">Identify mistakes in calculations.<\/a><\/li>\r\n<\/ul>\r\nYou will also have an opportunity to refresh the following skills:\r\n<ul>\r\n \t<li><a href=\"#name\">item.<\/a><\/li>\r\n \t<li><a href=\"#name\">item.<\/a><\/li>\r\n \t<li><a href=\"#name\">item.<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the next section of the course material and in the following activity, you will need to be familiar with a method for measuring how far a given data value is from the mean. You've seen before how to calculate deviation from the mean for a given data value. This method <em>standardizes<\/em> the distance in units of standard deviation above or below the mean.\u00a0The calculations will be performed by hand, and they can be a little tricky. In this corequisite support activity, you'll get some practice with them and learn where and how they can go wrong.\r\n<h2>Measuring Distance from Mean<\/h2>\r\nWe'll use a hypothetical typical arm span for Americans in our exploration of this method for measuring distance from the mean. Arm span is the distance from the tip of the middle finger on one hand to the tip of the middle finger on the other hand when one\u2019s arms are stretched out and opened wide.\r\n\r\nSuppose that, based on many measurements, a statistician believes that the distribution of arm spans of Americans has a mean of 173.40 centimeters (cm) and a standard deviation of 12.21 cm. Let's understand that these values to pertain to the population of all American arm spans (not just a sample).\r\n\r\nFor Questions 1, 3, and 5 below, you'll calculate arm span values that are one, two, and one-and-a-half standard deviations <strong>above and below<\/strong> the mean of 173.40 cm. Then, you'll carefully follow the directions in\u00a0Questions 2, 4, and 6, to make the specified calculations for each of the numbers you calculated in the previous question. Note that in each of these, you'll have found the difference between the given value and the mean, and divided that distance by the standard deviation.\u00a0 We call this\u00a0<em>standardizing the value<\/em>, but\u00a0 we'll cover that more deeply in the next section. For now, let's just get some practice making the necessary calculations by hand.\r\n<h3 id=\"InterpretStdDevUnits\">Calculate and interpret units of standard deviation as a measure of distance<\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nWhat arm span value is one standard deviation <strong>above<\/strong> the mean? What arm span value is one standard deviation <strong>below<\/strong> the mean? Round to the nearest hundredth.\r\n\r\n[reveal-answer q=\"315864\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"315864\"]The mean is 173.40 cm and one standard deviation is 12.21 cm[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\nFor each of the two answers you computed in Question 1, subtract the mean of 173.40 and then divide by the standard deviation of 12.21. In other words, calculate the following <strong>for each value<\/strong> computed in Question 1:\r\n\r\n[latex]\\dfrac{\\text{ Value }-173.4}{12.21}[\/latex]\r\n\r\n[reveal-answer q=\"844605\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"844605\"]Follow the example formula, replacing the value you obtained from the previous question, first for the value above the mean, then separately for the value below the mean. That is, make two separate calculations.[\/hidden-answer]\r\n\r\n<\/div>\r\nIn Question 1 you calculated a value exactly one standard deviation above and one below the mean. In Question 2, you divided the difference between the value you calculated and the mean by the standard deviation. You should have obtained positive one and negative one for the values above and below, respectively. What does positive imply? How about negative?\r\n\r\nLet's try another couple of sets of questions like that to observe what's happening.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\nWhat arm span value is two standard deviations <strong>above<\/strong> the mean? What arm span value is two standard deviations <strong>below<\/strong> the mean? Round to the nearest hundredth.\r\n\r\n[reveal-answer q=\"425088\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"425088\"]The mean is 173.40 cm and one standard deviation is 12.21 cm, so you can add or subtract [latex]2\\times12.21[\/latex] to the mean as needed.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\nFor each of the two answers you computed in Question 3, subtract the mean of 173.40 and then divide by the standard deviation of 12.21. In other words, calculate the following <strong>for each value<\/strong> computed in Question 3:\r\n\r\n[latex]\\dfrac{\\text{ Value }-173.4}{12.21}[\/latex]\r\n\r\n[reveal-answer q=\"316771\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"316771\"]Follow the example formula, replacing the value you obtained from the previous question, first for the value above the mean, then separately for the value below the mean. That is, make two separate calculations.[\/hidden-answer]\r\n\r\n<\/div>\r\nHopefully you obtained positive and negative two for your answers to Question 4. Have you caught on to what's happening in these question pairs yet?\u00a0 Let's try one more pair. In Question 5, you'll identify values one and a half standard deviations above and below the mean. Can you predict what the answers to Question 6 should be?\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\nWhat arm span value is one and a half standard deviations <strong>above<\/strong> the mean? What arm span value is one and a half standard deviations <strong>below<\/strong> the mean? Round to the nearest hundredth.\r\n\r\n[reveal-answer q=\"483705\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"483705\"]The mean is 173.40 cm and one standard deviation is 12.21 cm, so you can add or subtract [latex]1.5\\times12.21[\/latex] to the mean as needed.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\nFor each value computed in Question 5, calculate the following:\r\n\r\n[latex]\\dfrac{\\text{ Value } -173.4}{12.21}[\/latex]\r\n\r\n[reveal-answer q=\"125875\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"125875\"]Follow the example formula, replacing the value you obtained from the previous question, first for the value above the mean, then separately for the value below the mean. That is, make two separate calculations.[\/hidden-answer]\r\n\r\n<\/div>\r\nIn Questions 2, 4, and 6, you calculated values that were a given number of standard deviations above and below the mean. You discovered when you divided the difference between the value and the mean by the standard deviation, that the result was a positive number of standard deviations (for values above the mean) or a negative number of standard deviations (for values below the mean). That is, a resulting negative can be thought of as indicating a value that lies\u00a0<em>to the left<\/em> of the mean, and the positive indicates a value that lies\u00a0<em>to the right<\/em> of the mean.\r\n<h3 id=\"CalcDistStdDev\">Calculate the distance in units of standard deviations of an observed value from the population mean<\/h3>\r\nA natural question to consider might be, given any value any distance from the mean in any direction, if we find the difference between the value and mean, then divide by the standard deviation, would we be able to discover the number of standard deviations any value is from the mean and whether it lies to the right or to the left? Answer Questions 7 and 8 to explore this idea.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\nSuppose a classmate has an arm span of 200 cm. How many standard deviations from the mean is this arm span and in what direction? Round your answer to the nearest hundredth.\r\n\r\n[reveal-answer q=\"914574\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"914574\"]Find the difference (value - mean) divided by (standard deviation)[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 8<\/h3>\r\nSuppose another classmate has an arm span of 165 cm. How many standard deviations from the mean is this arm span and in what direction?\u00a0Round your answer to the nearest hundredth.\r\n\r\n[reveal-answer q=\"55941\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"55941\"]Find the difference (value - mean) divided by (standard deviation)[\/hidden-answer]\r\n\r\n<\/div>\r\nNow let's spend some time understanding how and in what way these kinds of calculations can go wrong.\r\n<h3 id=\"IdentMistakes\">Identify mistakes in calculations<\/h3>\r\nSuppose the statistician making these calculations thought she was using her calculator correctly, but in three different attempts, she arrived at three different answers. The three potential answers to her computational problem are shown below in Questions 9, 10, and 11 rounded to the nearest hundredth. For each, decide if it was computed correctly or, if not, explain what went wrong. Please refer to the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Order+of+Operations.pdf\">Order of Operations<\/a> Student Resource as needed.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 9<\/h3>\r\n[latex]\\dfrac{185-173.4}{12.21}\\approx 170.80[\/latex]\r\n\r\n[reveal-answer q=\"923550\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"923550\"]Consider how order of operation may have gone wrong.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 10<\/h3>\r\n[latex]\\dfrac{185-173.4}{12.21}\\approx -0.95[\/latex]\r\n\r\n[reveal-answer q=\"653940\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"653940\"]Should this answer be negative or positive?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 11<\/h3>\r\n[latex]\\dfrac{185-173.4}{12.21}\\approx 0.95[\/latex]\r\n\r\n[reveal-answer q=\"122468\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"122468\"]Does this answer appear to be incorrect?[\/hidden-answer]\r\n\r\n<\/div>\r\nQuestions 12, 13, and 14 below show three potential answers to a similar computational problem, rounded to the nearest hundredth. This time, the units of measure are included. For each, decide if it was computed correctly or, if not, explain what went wrong.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 12<\/h3>\r\n[latex]\\dfrac{150\\text{ cm }-173.4\\text{ cm }}{12.21\\text{ cm }}\\approx -1.92[\/latex]\r\n\r\n[reveal-answer q=\"362651\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"362651\"]Does this answer appear to be incorrect?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 13<\/h3>\r\n[latex]\\dfrac{150\\text{ cm }-173.4\\text{ cm }}{12.21\\text{ cm }}\\approx 1.92[\/latex]\r\n\r\n[reveal-answer q=\"409560\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"409560\"]Should this answer be positive or negative?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 14<\/h3>\r\n[latex]\\dfrac{150\\text{ cm }-173.4\\text{ cm }}{12.21\\text{ cm }}\\approx -1.92\\text{ cm }[\/latex]\r\n\r\n[reveal-answer q=\"281788\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"281788\"]Should the units cancel out? What units should the answer be in? [\/hidden-answer]\r\n\r\n<\/div>\r\nNow that you've had some practice making these calculations and learning how they can go wrong, it's time to move on to the next section.\r\n\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>What you&#8217;ll need to know<\/h3>\n<p>In this support activity you&#8217;ll become familiar with the following:<\/p>\n<ul>\n<li><a href=\"#InterpretStdDevUnits\">Calculate and interpret units of standard deviation as a measure of distance.<\/a><\/li>\n<li><a href=\"#CalcDistStdDev\">Calculate the distance in units of standard deviations of an observed value from the population mean.<\/a><\/li>\n<li><a href=\"#IdentMistakes\">Identify mistakes in calculations.<\/a><\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><a href=\"#name\">item.<\/a><\/li>\n<li><a href=\"#name\">item.<\/a><\/li>\n<li><a href=\"#name\">item.<\/a><\/li>\n<\/ul>\n<\/div>\n<p>In the next section of the course material and in the following activity, you will need to be familiar with a method for measuring how far a given data value is from the mean. You&#8217;ve seen before how to calculate deviation from the mean for a given data value. This method <em>standardizes<\/em> the distance in units of standard deviation above or below the mean.\u00a0The calculations will be performed by hand, and they can be a little tricky. In this corequisite support activity, you&#8217;ll get some practice with them and learn where and how they can go wrong.<\/p>\n<h2>Measuring Distance from Mean<\/h2>\n<p>We&#8217;ll use a hypothetical typical arm span for Americans in our exploration of this method for measuring distance from the mean. Arm span is the distance from the tip of the middle finger on one hand to the tip of the middle finger on the other hand when one\u2019s arms are stretched out and opened wide.<\/p>\n<p>Suppose that, based on many measurements, a statistician believes that the distribution of arm spans of Americans has a mean of 173.40 centimeters (cm) and a standard deviation of 12.21 cm. Let&#8217;s understand that these values to pertain to the population of all American arm spans (not just a sample).<\/p>\n<p>For Questions 1, 3, and 5 below, you&#8217;ll calculate arm span values that are one, two, and one-and-a-half standard deviations <strong>above and below<\/strong> the mean of 173.40 cm. Then, you&#8217;ll carefully follow the directions in\u00a0Questions 2, 4, and 6, to make the specified calculations for each of the numbers you calculated in the previous question. Note that in each of these, you&#8217;ll have found the difference between the given value and the mean, and divided that distance by the standard deviation.\u00a0 We call this\u00a0<em>standardizing the value<\/em>, but\u00a0 we&#8217;ll cover that more deeply in the next section. For now, let&#8217;s just get some practice making the necessary calculations by hand.<\/p>\n<h3 id=\"InterpretStdDevUnits\">Calculate and interpret units of standard deviation as a measure of distance<\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>What arm span value is one standard deviation <strong>above<\/strong> the mean? What arm span value is one standard deviation <strong>below<\/strong> the mean? Round to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q315864\">Hint<\/span><\/p>\n<div id=\"q315864\" class=\"hidden-answer\" style=\"display: none\">The mean is 173.40 cm and one standard deviation is 12.21 cm<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p>For each of the two answers you computed in Question 1, subtract the mean of 173.40 and then divide by the standard deviation of 12.21. In other words, calculate the following <strong>for each value<\/strong> computed in Question 1:<\/p>\n<p>[latex]\\dfrac{\\text{ Value }-173.4}{12.21}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q844605\">Hint<\/span><\/p>\n<div id=\"q844605\" class=\"hidden-answer\" style=\"display: none\">Follow the example formula, replacing the value you obtained from the previous question, first for the value above the mean, then separately for the value below the mean. That is, make two separate calculations.<\/div>\n<\/div>\n<\/div>\n<p>In Question 1 you calculated a value exactly one standard deviation above and one below the mean. In Question 2, you divided the difference between the value you calculated and the mean by the standard deviation. You should have obtained positive one and negative one for the values above and below, respectively. What does positive imply? How about negative?<\/p>\n<p>Let&#8217;s try another couple of sets of questions like that to observe what&#8217;s happening.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p>What arm span value is two standard deviations <strong>above<\/strong> the mean? What arm span value is two standard deviations <strong>below<\/strong> the mean? Round to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q425088\">Hint<\/span><\/p>\n<div id=\"q425088\" class=\"hidden-answer\" style=\"display: none\">The mean is 173.40 cm and one standard deviation is 12.21 cm, so you can add or subtract [latex]2\\times12.21[\/latex] to the mean as needed.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p>For each of the two answers you computed in Question 3, subtract the mean of 173.40 and then divide by the standard deviation of 12.21. In other words, calculate the following <strong>for each value<\/strong> computed in Question 3:<\/p>\n<p>[latex]\\dfrac{\\text{ Value }-173.4}{12.21}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q316771\">Hint<\/span><\/p>\n<div id=\"q316771\" class=\"hidden-answer\" style=\"display: none\">Follow the example formula, replacing the value you obtained from the previous question, first for the value above the mean, then separately for the value below the mean. That is, make two separate calculations.<\/div>\n<\/div>\n<\/div>\n<p>Hopefully you obtained positive and negative two for your answers to Question 4. Have you caught on to what&#8217;s happening in these question pairs yet?\u00a0 Let&#8217;s try one more pair. In Question 5, you&#8217;ll identify values one and a half standard deviations above and below the mean. Can you predict what the answers to Question 6 should be?<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p>What arm span value is one and a half standard deviations <strong>above<\/strong> the mean? What arm span value is one and a half standard deviations <strong>below<\/strong> the mean? Round to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q483705\">Hint<\/span><\/p>\n<div id=\"q483705\" class=\"hidden-answer\" style=\"display: none\">The mean is 173.40 cm and one standard deviation is 12.21 cm, so you can add or subtract [latex]1.5\\times12.21[\/latex] to the mean as needed.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p>For each value computed in Question 5, calculate the following:<\/p>\n<p>[latex]\\dfrac{\\text{ Value } -173.4}{12.21}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q125875\">Hint<\/span><\/p>\n<div id=\"q125875\" class=\"hidden-answer\" style=\"display: none\">Follow the example formula, replacing the value you obtained from the previous question, first for the value above the mean, then separately for the value below the mean. That is, make two separate calculations.<\/div>\n<\/div>\n<\/div>\n<p>In Questions 2, 4, and 6, you calculated values that were a given number of standard deviations above and below the mean. You discovered when you divided the difference between the value and the mean by the standard deviation, that the result was a positive number of standard deviations (for values above the mean) or a negative number of standard deviations (for values below the mean). That is, a resulting negative can be thought of as indicating a value that lies\u00a0<em>to the left<\/em> of the mean, and the positive indicates a value that lies\u00a0<em>to the right<\/em> of the mean.<\/p>\n<h3 id=\"CalcDistStdDev\">Calculate the distance in units of standard deviations of an observed value from the population mean<\/h3>\n<p>A natural question to consider might be, given any value any distance from the mean in any direction, if we find the difference between the value and mean, then divide by the standard deviation, would we be able to discover the number of standard deviations any value is from the mean and whether it lies to the right or to the left? Answer Questions 7 and 8 to explore this idea.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p>Suppose a classmate has an arm span of 200 cm. How many standard deviations from the mean is this arm span and in what direction? Round your answer to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q914574\">Hint<\/span><\/p>\n<div id=\"q914574\" class=\"hidden-answer\" style=\"display: none\">Find the difference (value &#8211; mean) divided by (standard deviation)<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p>Suppose another classmate has an arm span of 165 cm. How many standard deviations from the mean is this arm span and in what direction?\u00a0Round your answer to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q55941\">Hint<\/span><\/p>\n<div id=\"q55941\" class=\"hidden-answer\" style=\"display: none\">Find the difference (value &#8211; mean) divided by (standard deviation)<\/div>\n<\/div>\n<\/div>\n<p>Now let&#8217;s spend some time understanding how and in what way these kinds of calculations can go wrong.<\/p>\n<h3 id=\"IdentMistakes\">Identify mistakes in calculations<\/h3>\n<p>Suppose the statistician making these calculations thought she was using her calculator correctly, but in three different attempts, she arrived at three different answers. The three potential answers to her computational problem are shown below in Questions 9, 10, and 11 rounded to the nearest hundredth. For each, decide if it was computed correctly or, if not, explain what went wrong. Please refer to the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Order+of+Operations.pdf\">Order of Operations<\/a> Student Resource as needed.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 9<\/h3>\n<p>[latex]\\dfrac{185-173.4}{12.21}\\approx 170.80[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q923550\">Hint<\/span><\/p>\n<div id=\"q923550\" class=\"hidden-answer\" style=\"display: none\">Consider how order of operation may have gone wrong.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 10<\/h3>\n<p>[latex]\\dfrac{185-173.4}{12.21}\\approx -0.95[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q653940\">Hint<\/span><\/p>\n<div id=\"q653940\" class=\"hidden-answer\" style=\"display: none\">Should this answer be negative or positive?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 11<\/h3>\n<p>[latex]\\dfrac{185-173.4}{12.21}\\approx 0.95[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q122468\">Hint<\/span><\/p>\n<div id=\"q122468\" class=\"hidden-answer\" style=\"display: none\">Does this answer appear to be incorrect?<\/div>\n<\/div>\n<\/div>\n<p>Questions 12, 13, and 14 below show three potential answers to a similar computational problem, rounded to the nearest hundredth. This time, the units of measure are included. For each, decide if it was computed correctly or, if not, explain what went wrong.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 12<\/h3>\n<p>[latex]\\dfrac{150\\text{ cm }-173.4\\text{ cm }}{12.21\\text{ cm }}\\approx -1.92[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q362651\">Hint<\/span><\/p>\n<div id=\"q362651\" class=\"hidden-answer\" style=\"display: none\">Does this answer appear to be incorrect?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 13<\/h3>\n<p>[latex]\\dfrac{150\\text{ cm }-173.4\\text{ cm }}{12.21\\text{ cm }}\\approx 1.92[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q409560\">Hint<\/span><\/p>\n<div id=\"q409560\" class=\"hidden-answer\" style=\"display: none\">Should this answer be positive or negative?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 14<\/h3>\n<p>[latex]\\dfrac{150\\text{ cm }-173.4\\text{ cm }}{12.21\\text{ cm }}\\approx -1.92\\text{ cm }[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q281788\">Hint<\/span><\/p>\n<div id=\"q281788\" class=\"hidden-answer\" style=\"display: none\">Should the units cancel out? What units should the answer be in? <\/div>\n<\/div>\n<\/div>\n<p>Now that you&#8217;ve had some practice making these calculations and learning how they can go wrong, it&#8217;s time to move on to the next section.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"author":25777,"menu_order":30,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-492","chapter","type-chapter","status-publish","hentry"],"part":621,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":31,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/492\/revisions"}],"predecessor-version":[{"id":3325,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/492\/revisions\/3325"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/621"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/492\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=492"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=492"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=492"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}