{"id":164,"date":"2022-04-12T12:17:04","date_gmt":"2022-04-12T12:17:04","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=164"},"modified":"2024-11-28T07:26:11","modified_gmt":"2024-11-28T07:26:11","slug":"h-11-estimate-population-size-using-proportions","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/h-11-estimate-population-size-using-proportions\/","title":{"rendered":"H.11 Estimate population size using proportions"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" 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-large-font-size wp-elements-7c63c222c7d5cfd9bc5debab76ae607b\" style=\"color:#74008b\"><strong>Key notes : <\/strong>&#8211;<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-146cc463ec783a38376ce04cb5468194\" style=\"color:#000060\">1. <strong>Understanding Population and Sample<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Population<\/strong>: The entire group that is being studied.<\/li>\n\n\n\n<li><strong>Sample<\/strong>: A smaller group selected from the population that represents the population.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-33b62cec46115201a88531f14d07e547\" style=\"color:#000060\">2. <strong>Why Estimate Population Size?<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Estimating the population size is important when it&#8217;s impractical or impossible to count every individual in a large population, like animals in the wild, or people in a large city.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-7e74e2a4613b5effd75680dc5e7eba5c\" style=\"color:#000060\">3. <strong>Proportions in Estimation<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>The principle behind estimating population size using proportions is based on the idea that if you know the proportion of a sample, you can use that proportion to estimate the entire population&#8217;s size.<\/li>\n\n\n\n<li><strong>Proportion Formula<\/strong>:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"820\" height=\"76\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-202.png\" alt=\"\" class=\"wp-image-19132\" style=\"width:658px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-202.png 820w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-202-300x28.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-202-768x71.png 768w\" sizes=\"auto, (max-width: 820px) 100vw, 820px\" \/><\/figure><\/div>\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Proportion Setup<\/strong>:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"457\" height=\"66\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-203.png\" alt=\"\" class=\"wp-image-19133\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-203.png 457w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-203-300x43.png 300w\" sizes=\"auto, (max-width: 457px) 100vw, 457px\" \/><\/figure><\/div>\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\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#97f9ca\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-fea6b6b8e15a28f0f85c3609a7311032\" style=\"color:#b00012\"><strong>\ud83d\udd34To determine the bobcat population, scientists tagged 81 bobcats. Later, they counted 700 bobcats, of which 27 had tags. To the nearest whole number, what is the best estimate for the bobcat population?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udd37The ratio of marked bobcats to total bobcats should be about the same in both the sample population and the overall population. You know how many bobcats were in the sample and how many of those were marked. You also know the total number of marked bobcats.<\/li>\n\n\n\n<li>Set up a proportion.\n<ul class=\"wp-block-list\">\n<li>marked bobcats counted \/ total bobcats counted = total marked bobcats \/ estimated bobcat population<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Plug in the numbers you know and solve for the bobcat population,&nbsp;<em>p<\/em>.<\/li>\n\n\n\n<li>27\/100 = 81\/p<\/li>\n\n\n\n<li>27\/100 ( 700p ) = 81\/p ( 700p ) &#8212;&#8211;&gt; Multiply both sides by 700p<\/li>\n\n\n\n<li>27p = 81 \u00b7 700 &#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>27p = 56,700 &#8212;&#8212;&#8211;&gt; Simplify<\/li>\n\n\n\n<li>p = 2,100 &#8212;&#8212;&#8212;&gt; Divide both sides by 27<\/li>\n\n\n\n<li>The best estimate for the bobcat population is 2,100.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#eea2b2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-7d84df561a92b840735446d24f4c84b9\" style=\"color:#b00012\"><strong>\ud83d\udd34 Scientists captured, tagged, and released 36 crows as part of a research study. A week later, they counted 180 crows, of which 27 had tags. To the nearest whole number, what is the best estimate for the crow population?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udd37The ratio of marked crows to total crows should be about the same in both the sample population and the overall population. You know how many crows were in the sample and how many of those were marked. You also know the total number of marked crows.<\/li>\n\n\n\n<li>Set up a proportion.\n<ul class=\"wp-block-list\">\n<li>marked crows counted \/ total crows counted = total marked crows \/ estimated crow population<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Plug in the numbers you know and solve for the crow population,&nbsp;<em>p<\/em>.<\/li>\n\n\n\n<li>27\/180 = 36\/p<\/li>\n\n\n\n<li>27\/180 ( 180p ) = 36\/p ( 180p ) &#8212;&#8212;&#8212;&gt; Multiply both sides by 180p<\/li>\n\n\n\n<li>27p = 36 \u00b7 180 &#8212;&#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>27p = 6,480 &#8212;&#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>p = 240 &#8212;&#8212;&#8211;&gt; Divide both sides by 27<\/li>\n\n\n\n<li>The best estimate for the crow population is 240.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#73caf6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-4f68a94502f307c92809936e4eb0e7fb\" style=\"color:#b00012\"><strong>\ud83d\udd34 Wombats are animals that are native to Australia and are related to kangaroos. To estimate the wombat population, Professor Roth&#8217;s research group trapped 89 wombats and tagged them. They returned the tagged wombat to the wild, and a week later, trapped 240 wombats. Of those wombats, 24 were marked. To the nearest whole number, what is the best estimate for the wombat population?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udd37 The ratio of marked wombats to total wombats should be about the same in both the sample population and the overall population. You know how many wombats were in the sample and how many of those were marked. You also know the total number of marked wombats.<\/li>\n\n\n\n<li>Set up a proportion.\n<ul class=\"wp-block-list\">\n<li>marked wombats counted \/ total wombats counted = total marked wombats \/ estimated wombat population<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Plug in the numbers you know and solve for the wombat population, p.<\/li>\n\n\n\n<li>24\/240 = 89\/p<\/li>\n\n\n\n<li>24\/240 ( 240p ) = 89\/p ( 240p ) &#8212;&#8212;-&gt; Multiply both sides by 240p<\/li>\n\n\n\n<li>24p = 89 \u00b7 240 &#8212;&#8212;&#8211;&gt; Simplify <\/li>\n\n\n\n<li>24p = 21,360 &#8212;&#8212;&#8211;&gt; Simplify<\/li>\n\n\n\n<li>p = 890 &#8212;&#8212;&#8211;&gt; Divide both sides by 24<\/li>\n\n\n\n<li>The best estimate for the wombat population is 890.<\/li>\n<\/ul>\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<\/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\/81272\/296\/400\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-320.png\" alt=\"\" class=\"wp-image-9676\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-320.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-320-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-320-150x150.png 150w\" 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\/81430\/846\/789\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-328.png\" alt=\"\" class=\"wp-image-9677\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-328.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-328-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-328-150x150.png 150w\" 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 notes : &#8211; 1. Understanding Population and Sample 2. Why Estimate Population Size? 3. Proportions in Estimation Learn with an example \ud83d\udd34To determine the bobcat population, scientists tagged 81 bobcats. Later, they counted 700 bobcats, of which 27 had tags. To the nearest whole number, what is the best<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/h-11-estimate-population-size-using-proportions\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.11 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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-164","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=164"}],"version-history":[{"count":21,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164\/revisions"}],"predecessor-version":[{"id":19284,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164\/revisions\/19284"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}