{"id":214,"date":"2022-04-12T09:54:36","date_gmt":"2022-04-12T09:54:36","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=214"},"modified":"2025-12-19T05:36:31","modified_gmt":"2025-12-19T05:36:31","slug":"j-12-estimate-population-size-using-proportions","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/j-12-estimate-population-size-using-proportions\/","title":{"rendered":"J.12 Estimate population size using proportions"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Estimate population size using proportions<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-d4d355b76dd54277399098c306fb7fdd\" style=\"color:#74008b\">key points :<\/p>\n\n\n\n<p class=\"has-large-font-size\">\ud83d\udd22 <strong>What is Estimating Population Size?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It means <strong>finding an approximate number<\/strong> of people, animals, or objects in a large group.<\/li>\n\n\n\n<li>We use <strong>samples<\/strong> and <strong>proportions<\/strong> instead of counting everyone.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">\ud83d\udce6 <strong>What is a Sample?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>sample<\/strong> is a small part of the whole population.<\/li>\n\n\n\n<li>It should be <strong>fair and random<\/strong> \ud83c\udfaf so it represents the whole group.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">\ud83d\udcca <strong>What is a Proportion?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>proportion<\/strong> compares a part to the whole.<\/li>\n\n\n\n<li>Written as a fraction, ratio, or percentage (e.g., 3\/10, 3:10, 30%).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">\ud83d\udd01 <strong>Why Use Proportions?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Counting large populations is <strong>hard and time-consuming<\/strong> \u23f3<\/li>\n\n\n\n<li>Proportions help us <strong>estimate quickly and easily<\/strong> \u26a1<\/li>\n<\/ul>\n\n\n\n<p>\ud83e\uddee <strong>Steps to Estimate Population Size<\/strong><br>1\ufe0f\u20e3 Choose a <strong>random sample<\/strong> from the population<br>2\ufe0f\u20e3 Count the number with a <strong>specific feature<\/strong><br>3\ufe0f\u20e3 Write the <strong>proportion<\/strong><br>4\ufe0f\u20e3 Use the same proportion to estimate the <strong>total population<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">\ud83d\udcd8 <strong>Simple Example<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In a sample of <strong>20 students<\/strong>, <strong>5 wear glasses<\/strong> \ud83d\udc53<\/li>\n\n\n\n<li>Proportion = 5\/20 = 1\/4<\/li>\n\n\n\n<li>If the whole school has <strong>400 students<\/strong><\/li>\n\n\n\n<li>Estimated students with glasses = 1\/4 \u00d7 400 = <strong>100<\/strong> \ud83c\udf89<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">\ud83c\udf31 <strong>Real-Life Uses<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Counting <strong>fish in a pond<\/strong> \ud83d\udc1f<\/li>\n\n\n\n<li>Estimating <strong>tree population in a forest<\/strong> \ud83c\udf33<\/li>\n\n\n\n<li>Finding number of <strong>people in a city<\/strong> \ud83c\udfd9\ufe0f<\/li>\n\n\n\n<li>Studying <strong>wildlife and environment<\/strong> \ud83e\udd8b<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">\u26a0\ufe0f <strong>Remember!<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>better the sample<\/strong>, the <strong>better the estimate<\/strong> \u2705<\/li>\n\n\n\n<li>Estimates are <strong>close values<\/strong>, not exact numbers \ud83c\udfaf<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-large-font-size\">\ud83c\udfa8 <strong>Quick Tip for Students:<\/strong><\/p>\n\n\n\n<p>\ud83d\udc49 Think <strong>small \u2192 big<\/strong> using proportions!<br>\ud83d\udc49 Sample smartly and estimate confidently \ud83d\ude04\ud83d\udcd0<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background\" style=\"background-color:#d5f8e1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u270f\ufe0f <strong>For a research project on the local skunk population, 120 skunks were tagged and set free. Later, volunteers returned to the site and found 18 tagged skunks out the 450 skunks they counted. To the nearest whole number, what is the best estimate for the skunk population?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>The ratio of marked skunks to total skunks should be about the same in both the sample population and the overall population. You know how many skunks were in the sample and how many of those were marked. You also know the total number of marked skunks.<\/p>\n\n\n\n<p>marked skunks counted \/ total skunks counted = total marked skunks \/ estimated skunk population<\/p>\n\n\n\n<p>Plug in the numbers you know and solve for the skunk population,&nbsp;<em>p<\/em>.<\/p>\n\n\n\n<p>18\/450 = 120\/p<\/p>\n\n\n\n<p>18\/450 ( 450p ) = 120\/p ( 450p )            Multiply both sides by 450p<\/p>\n\n\n\n<p>18p = 120 \u00b7 450                    Simplify<\/p>\n\n\n\n<p>18p = 54,000                     Simplify<\/p>\n\n\n\n<p>p = 3,000                         Divide both sides by 18<\/p>\n\n\n\n<p>The best estimate for the skunk population is 3,000.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#ecd4fb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u270f\ufe0f <strong>For a research study on various types of lizards, scientists wanted to estimate the local skink population. They captured, marked, and released 26 skinks. A week later, the scientists returned to the site and found 10 marked skinks out of the 150 skinks they counted. To the nearest whole number, what is the best estimate for the skink population?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>The ratio of marked skinks to total skinks should be about the same in both the sample population and the overall population. You know how many skinks were in the sample and how many of those were marked. You also know the total number of marked skinks.<\/p>\n\n\n\n<p>Set up a proportion.<\/p>\n\n\n\n<p>marked skinks counted \/ total skinks counted = total marked skinks \/ estimated skink population<\/p>\n\n\n\n<p>Plug in the numbers you know and solve for the skink population,&nbsp;<em>p<\/em>.<\/p>\n\n\n\n<p>10\/150 = 26\/p<\/p>\n\n\n\n<p>10\/150 ( 150p ) = 26\/p ( 150p )                 Multiply both sides by 150p<\/p>\n\n\n\n<p>10p = 26 \u00b7 150                    Simplify<\/p>\n\n\n\n<p>10p = 3,900                     Simplify<\/p>\n\n\n\n<p>p = 390                         Divide both sides by 10<\/p>\n\n\n\n<p>The best estimate for the skink population is 390.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f8f3cc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u270f\ufe0f <strong>For a science fair project, a group of students decides to estimate the population of hedgehogs living in the nearby forest. They trap 69 hedgehogs and mark them. Then, a week later, they return to the forest and trap 1,000 hedgehogs, 23 of which are marked. To the nearest whole number, what is the best estimate for the hedgehog population?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>The ratio of marked hedgehogs to total hedgehogs should be about the same in both the sample population and the overall population. You know how many hedgehogs were in the sample and how many of those were marked. You also know the total number of marked hedgehogs.<\/p>\n\n\n\n<p>Set up a proportion.<\/p>\n\n\n\n<p>marked hedgehogs counted \/ total hedgehogs counted = total marked hedgehogs \/ estimated hedgehog population<\/p>\n\n\n\n<p>Plug in the numbers you know and solve for the hedgehog population,&nbsp;<em>p<\/em>.<\/p>\n\n\n\n<p>23\/1000 = 69\/p<\/p>\n\n\n\n<p>23\/1000 ( 1000p ) = 69\/p ( 1000p )                Multiply both sides by 1,000p<\/p>\n\n\n\n<p>23p = 69 \u00b7 1,000                     Simplify<\/p>\n\n\n\n<p>23p = 69,000                       Simplify<\/p>\n\n\n\n<p>p = 3,000                          Divide both sides by 23<\/p>\n\n\n\n<p>The best estimate for the hedgehog population is 3,000.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice! \ud83d\udd8a\ufe0f<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/86000\/869\/283\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-305.png\" alt=\"\" class=\"wp-image-7540\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-305.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-305-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-305-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-305-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/31241\/650\/358\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-315.png\" alt=\"\" class=\"wp-image-7541\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-315.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-315-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-315-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-315-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Estimate population size using proportions key points : \ud83d\udd22 What is Estimating Population Size? \ud83d\udce6 What is a Sample? \ud83d\udcca What is a Proportion? \ud83d\udd01 Why Use Proportions? \ud83e\uddee Steps to Estimate Population Size1\ufe0f\u20e3 Choose a random sample from the population2\ufe0f\u20e3 Count the number with a specific feature3\ufe0f\u20e3 Write the proportion4\ufe0f\u20e3 Use the same proportion<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/j-12-estimate-population-size-using-proportions\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.12 Estimate population size using proportions&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-214","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/214","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=214"}],"version-history":[{"count":13,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/214\/revisions"}],"predecessor-version":[{"id":17669,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/214\/revisions\/17669"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}