{"id":10,"date":"2017-08-18T07:19:34","date_gmt":"2017-08-18T07:19:34","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/chemistry\/?page_id=10"},"modified":"2017-09-18T13:54:17","modified_gmt":"2017-09-18T13:54:17","slug":"interpreting-and-measuring-data","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/chemistry\/interpreting-and-measuring-data\/","title":{"rendered":"Interpreting and Measuring Data"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\">\n<p><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/scientific-investigation\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/scientific-knowledge\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/scientific-knowledge-working-in-the-laboratory\">Next Lesson \u27a1<\/a><\/p>\n<\/div>\n<p><!-- UPDATE NEXT\/PREVIOUS ABOVE --><\/p>\n<p><!-- CONTENT STARTS HERE --><\/p>\n<h1 id=\"title\">Interpreting and Measuring Data<\/h1>\n<h4>Objective<\/h4>\n<p>In this lesson we will review measurement and calculation within science.<\/p>\n<section>\n<h4>Previously we covered&#8230;<\/h4>\n<ul>\n<li>Identifying the relationships between branches of science.<\/li>\n<li>Explaining scientific investigation.<\/li>\n<\/ul>\n<h3>Data<\/h3>\n<p><abbr title=\"Information collected during a scientific experiment\">Data<\/abbr> is the information collected during an experiment. This information could be weight, temperature, pH, or any other scientific investigative material. Since we have this information and we conducted the experiment, we understand the data we collected. However, how do we explain this data to someone else? How do we display this data so it can be easily read and interpreted? Many scientists use graphs to showcase data. There are many types of graphs or charts that may be utilized: line, bar, pie, diagrams, and sometimes even models or maps. In order to make it possible for our audience to understand our data, a legend and key for all of these types of data displays should be included. The most commonly used charts or graphs are a line graph, bar graph, and pie chart.<\/p>\n<p><abbr title=\"Summarize how two pieces of information are related and how they vary depending on one another\">Line graphs<\/abbr> are used to summarize how two pieces of information are related and how they vary depending on one another.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/interpetingdata2.linegraph.jpg\" \/><\/center><\/p>\n<p class=\"figcaption\">Example of a line graph used correctly to show the large impact of the 1997-1998 El Ni\u00f1o Southern Oscillation effect on precipitation on the island of New Guinea.<\/p>\n<p><abbr title=\"A graph that consists of an axis and a series of labeled horizontal or vertical bars that show different values for each bar; the numbers along a side of the bar graph are called the scale.\">Bar graphs<\/abbr> consist of an axis and a series of labeled horizontal or vertical bars that show different values for each bar. The numbers along a side of the bar graph are called the scale.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/interpretingdata2.bargraph.gif\" \/><\/center>This graph depicts how many sales were made by each division over a time period denoted by quarters. For this bar graph the <abbr title=\"The factor that is deliberately manipulated in an experiment\">independent variable<\/abbr> is plotted on the x-axis and the <abbr title=\"The variable that is changed or determined by manipulation of one or more factors\">dependent variable<\/abbr> is plotted on the y-axis. For bar graphs, the variables can be designated on either axis.<\/p>\n<p><abbr title=\"A circle graph divided into pieces displaying the parts that make up some whole\">Pie charts<\/abbr> are used to display the sizes of parts that make up some whole. A pie chart is a circle graph divided into pieces, each displaying the size of some related piece of information.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/interpretingdata2.piechart.jpg\" \/><\/center><\/p>\n<p class=\"figcaption\">This pie chart accurately shows the different numbers of frog clutches found in 1998. Each category is a separate micro-habitat where the frogs live and lay their eggs.<\/p>\n<p>Sometimes data must be depicted utilizing numbers. All numbers must be consistent. To accomplish this task, scientists use scientific notation.<\/p>\n<h3>Scientific Notation<\/h3>\n<p>Sometimes data must be depicted utilizing numbers. All numbers must be consistent. To accomplish this task, scientists use scientific notation. Scientists often deal with very small and very large numbers. These numbers are written as powers of 10. Scientific notation takes the form of M multiplication symbol 10<sup>n<\/sup> where 1 \u2264 M &lt; 10 and n represents the number of decimal places to be moved. Positive n indicates the standard form is a large number. Negative n indicates a number between zero and one.<\/p>\n<p>Example 1:<\/p>\n<p>To convert 4,500,000 to scientific notation, move the decimal point so that there is only one digit to its left, a total of 6 places.<\/p>\n<p class=\"center\">4,500,000 = 4.5 \u2217 10<sup>6<\/sup><\/p>\n<p>Example 2:<\/p>\n<p>To convert 0.000018 to scientific notation, move the decimal point 5 places to the right.<\/p>\n<p class=\"center\">0.000018 = 1.8 \u2217 10<sup>\u22125<\/sup><\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Express the following in scientific notation. 0.001 = _____<\/p>\n<p>Express the following in standard form. 1.1 \u2217 10<sup>3<\/sup> = _____<\/p>\n<div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">a) 0.001 = 1.0 \u2217 10<sup>\u22123<\/sup><\/p>\n<p class=\"q-reveal\">b) 1.1 \u2217 10<sup>3<\/sup> = 1,100<\/p>\n<\/div>\n<\/section>\n<h3>Significant Figures<\/h3>\n<p>A measurement can only be as accurate and precise as the instrument utilized. A scientist must be able to express the accuracy of a number, not just its numerical value. We can determine the accuracy of a number by the number of <abbr title=\"A prescribed decimal place that determines the amount of rounding off to be done based on the precision of a measurement\">significant figures<\/abbr> it contains.<\/p>\n<p>There are five rules governing significant figures:<\/p>\n<table>\n<thead>\n<tr>\n<th>Rule<\/th>\n<th>Example<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1. All digits 1-9 inclusive are significant.<\/td>\n<td>12 has 2 significant figures.<\/td>\n<\/tr>\n<tr>\n<td>2. Zeros between significant digits are always significant.<\/td>\n<td>10<sup>4<\/sup> has 3 significant figures.<\/td>\n<\/tr>\n<tr>\n<td>3. Trailing zeros in a number are significant ONLY if the number contains a decimal point.<\/td>\n<td>10 has 1 significant figure.<\/td>\n<\/tr>\n<tr>\n<td>4. Zeros in the beginning of a number whose only function is to place the decimal point are not significant.<\/td>\n<td>0.065 has 2 significant figures.<\/td>\n<\/tr>\n<tr>\n<td>5. Zeros following a decimal fraction\u2019s rightmost significant figure are significant.<\/td>\n<td>0.000123 has 3 significant figures.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>How many significant figures are in each number below?<\/p>\n<p>a) 500. _____<\/p>\n<p>b) 0.01 _____<\/p>\n<p>c) .005 _____<\/p>\n<div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">a) 500. has 3 significant figures<\/p>\n<p class=\"q-reveal\">b) 0.01 has 1 significant figure<\/p>\n<p class=\"q-reveal\">c) .005 has 1 significant figure<\/p>\n<\/div>\n<\/section>\n<h3>Accuracy and Precision<\/h3>\n<p>Scientists use numbers quite often during investigations. Math and science are very interrelated subjects. Previously, we discussed scientific notation and significant figures. Aside from utilizing those methods to display data, precise and accurate numbers should also be used. <abbr title=\"A description of how close a measurement is to the true value of the quantity measured\">Accuracy<\/abbr> is a description of how close a measurement is to the true value of the quantity measured. <abbr title=\"The exactness of a measurement\">Precision<\/abbr> is the exactness of a measurement.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/interpretingdata5.accuprec.png\" alt=\"targets depicting accuracy and precision\" \/><\/center><\/p>\n<h4>Mean, Median and Mode<\/h4>\n<p>Three other mathematical names that should be applied to numbers in scientific investigation are mean, median and mode.<\/p>\n<p><abbr title=\"The arithmetic average of a list of numbers found by summing and then dividing by the number of elements\">Mean<\/abbr> (also known as arithmetic average) is the average of a list of numbers. It is found by adding all the numbers in the list and dividing by the number of elements in the list.<\/p>\n<p><em>Example:<\/em> Find the mean of 5, 6, 9, and 8.<\/p>\n<p>We add all the numbers, and divide by the number of elements in the list, which is 4. (5 + 6 + 9 + 8) \u00f7 4 = 7<\/p>\n<p>So the mean of these four numbers is 7.<\/p>\n<p><abbr title=\"The middle number in a list of numbers found by ordering them from least to greatest\">Median<\/abbr> is the middle number in a list of numbers found by ordering them from least to greatest. If there is an odd number of numbers, the middle number in this ordering is the median. If there is an even number of numbers, the median is the sum of the two middle numbers, divided by 2.<\/p>\n<p><em>Example:<\/em> The night school program has students of various ages: 16, 14, 22, 16, 18, 15, and 20. What is the median of these ages? First you must place them in numerical order from least to greatest. 14, 15, 16, 16, 18, 20, 22.<\/p>\n<p>Then determine what the middle number is. If there is an even number of numbers, add the two middle numbers together and divide by 2. 16 is the median age of the students at the night school<\/p>\n<p><abbr title=\"The number that occurs most often in a list of numbers\">Mode<\/abbr> is the number that occurs most often in a list of numbers.<\/p>\n<p><em>Example:<\/em> All the biology classes have the following number of students registered: 35, 36, 36, 34 and 28. Find the mode for the biology classes.<\/p>\n<p>The mode is the number used most often. For this set of numbers it is 36.<\/p>\n<h3>International System (Systeme Internationale) of Units (SI Units)<\/h3>\n<p>In the scientific community, SI units are utilized worldwide. SI units are used for consistency. The SI system is based on the metric system and it contains seven basic units.<\/p>\n<table>\n<thead>\n<tr>\n<th colspan=\"3\">SI Units<\/th>\n<\/tr>\n<tr>\n<th>Quantity<\/th>\n<th>Unit<\/th>\n<th>Abbreviation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><abbr title=\"The straight-line distance between any two points\">Length<\/abbr><\/td>\n<td>meter<\/td>\n<td>m<\/td>\n<\/tr>\n<tr>\n<td><abbr title=\"How much matter an object has\">mass<\/abbr><\/td>\n<td>kilogram<\/td>\n<td>kg<\/td>\n<\/tr>\n<tr>\n<td><abbr title=\"A measure or record of the speed, duration, or rate of something\">Time<\/abbr><\/td>\n<td>second<\/td>\n<td>s<\/td>\n<\/tr>\n<tr>\n<td><abbr title=\"A measure of the average kinetic energy of all particles in an object\">Temperature<\/abbr><\/td>\n<td>kelvin<\/td>\n<td>K<\/td>\n<\/tr>\n<tr>\n<td><abbr title=\"The timed rate of flow of electric charge\">Electric current<\/abbr><\/td>\n<td>ampere<\/td>\n<td>A<\/td>\n<\/tr>\n<tr>\n<td><abbr title=\"How much of a substance exists\">Amount of substance<\/abbr><\/td>\n<td>mole<\/td>\n<td>mol<\/td>\n<\/tr>\n<tr>\n<td><abbr title=\"The luminous flux in lumens emitted per unit solid angle by a light source\">Luminous Intensity<\/abbr><\/td>\n<td>candela<\/td>\n<td>cd<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The above chart contains base units. However, sometimes the base unit is not the right unit to be utilized. For example: to weigh a book, you would measure it in kilograms; however, to weigh a pencil kilograms would be too large of a number. Since science does use the metric system, it is important to be able to convert from one unit to another. Prefixes are used for very large or very small numbers. Common prefixes and their amounts are listed below.<\/p>\n<table>\n<thead>\n<tr>\n<th colspan=\"9\">Prefixes<\/th>\n<\/tr>\n<tr>\n<th>mega<\/th>\n<th>kilo<\/th>\n<th>hecto<\/th>\n<th>deca<\/th>\n<th>BASE<\/th>\n<th>deci<\/th>\n<th>centi<\/th>\n<th>milli<\/th>\n<th>micro<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>M<\/td>\n<td>K<\/td>\n<td>H<\/td>\n<td>Da<\/td>\n<td>gram(g)<\/td>\n<td>d<\/td>\n<td>c<\/td>\n<td>m<\/td>\n<td>U<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>1,000,000<\/td>\n<td>1,000<\/td>\n<td>100<\/td>\n<td>10<\/td>\n<td>Liter(L)<\/td>\n<td>0.1<\/td>\n<td>0.01<\/td>\n<td>0.001<\/td>\n<td>0.000001<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>10<sup>6<\/sup><\/td>\n<td>10<sup>3<\/sup><\/td>\n<td>10<sup>2<\/sup><\/td>\n<td>10<\/td>\n<td>meter(m)<\/td>\n<td>10<sup>-1<\/sup><\/td>\n<td>10<sup>-2<\/sup><\/td>\n<td>10<sup>-3<\/sup><\/td>\n<td>10<sup>-6<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since science uses the metric system, it is important to be able to convert from one unit to another. The common formula used for translating between measurements is the <abbr title=\"Dimensional analysis used to convert between units\">factor label method<\/abbr>.<\/p>\n<h3>Factor Label Method:<\/h3>\n<ul>\n<li>Write the given number and unit.<\/li>\n<li>Set up a conversion factor (fraction used to convert one unit to another).\n<ul>\n<li>Place the given unit as denominator of the conversion factor.<\/li>\n<li>Place the desired unit as the numerator.<\/li>\n<li>Place a \u201c1\u201d in front of the larger unit.<\/li>\n<li>Determine the number of smaller units needed to make \u201c1\u201d of the larger unit.<\/li>\n<\/ul>\n<\/li>\n<li>Cancel units. Solve the problem.<\/li>\n<\/ul>\n<p><strong>Example:<\/strong><\/p>\n<p>45 mm = _____ m<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/interpretingdata7.factorlabel.png\" \/><\/center><\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Convert the following measurements using the factor label method.<\/p>\n<p>a) 9.50 g = _____ mg<\/p>\n<p>b) 45.0 km = _____ m<\/p>\n<div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">a) 9.50 g = 9500 mg<\/p>\n<p class=\"q-reveal\">b) 45.0 km = 45000 m<\/p>\n<div><\/div>\n<\/div>\n<\/section>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<p><!-- UPDATE NEXT\/PREVIOUS BELOW --><\/p>\n<div class=\"advance\">\n<p><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/scientific-investigation\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/scientific-knowledge\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/scientific-knowledge-working-in-the-laboratory\">Next Lesson \u27a1<\/a><\/p>\n<\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Interpreting and Measuring Data Objective In this lesson we will review measurement and calculation within science. Previously we covered&#8230; Identifying the relationships between branches of science. Explaining scientific investigation. Data Data is the information collected during an experiment. This information could be weight, temperature, pH, or any other scientific [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-10","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/10","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/comments?post=10"}],"version-history":[{"count":13,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/10\/revisions"}],"predecessor-version":[{"id":751,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/10\/revisions\/751"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/media?parent=10"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}