{"id":535,"date":"2022-04-13T05:28:06","date_gmt":"2022-04-13T05:28:06","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=535"},"modified":"2025-02-23T06:21:33","modified_gmt":"2025-02-23T06:21:33","slug":"z-14-pie-charts-and-central-angles","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/z-14-pie-charts-and-central-angles\/","title":{"rendered":"Z.14 Pie charts and central angles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Pie charts and central angles<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/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<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-7b0389a772b6c7cc35162352a772cb27\" style=\"color:#10d971\"><strong>1. Definition of a Pie Chart<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A pie chart is a circular chart divided into sectors (slices), each representing a proportion of the whole.<\/li>\n\n\n\n<li>The entire pie represents 100% of the data, and each sector\u2019s size is proportional to its share of the total.<\/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=\"318\" height=\"159\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-6.png\" alt=\"\" class=\"wp-image-17259\" style=\"width:546px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-6.png 318w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-6-300x150.png 300w\" sizes=\"auto, (max-width: 318px) 100vw, 318px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-99f480b4338fc94b1373265628454924\" style=\"color:#df1919\"><strong>2. Components of a Pie Chart<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Circle (Whole)<\/strong>: Represents the total dataset or 100%.<\/li>\n\n\n\n<li><strong>Sectors (Slices)<\/strong>: Each sector represents a category, showing its proportion relative to the whole.<\/li>\n\n\n\n<li><strong>Labels<\/strong>: Each sector may be labeled with the category name and its corresponding percentage or fraction of the whole.<\/li>\n\n\n\n<li><strong>Legend<\/strong>: Explains the categories represented by each sector, often using colors or patterns.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-f1dd96b543b88dba46cca18d005c1c4c\" style=\"color:#f20909\"><strong>3. Understanding Central Angles<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Central Angle<\/strong>: The angle formed at the center of the pie chart by two radii (lines from the center to the edge of the circle) that define a sector.<\/li>\n\n\n\n<li>The size of each central angle is directly proportional to the size of the sector and the proportion of the data it represents.<\/li>\n\n\n\n<li><strong>Total Central Angles<\/strong>: The sum of all central angles in a pie chart is 360\u00b0 because the chart is a complete circle.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-28c182bbc0bf7a1075606bbad92e536b\" style=\"color:#e6c20f\"><strong>4. Calculating Central Angles<\/strong><\/h3>\n\n\n\n<p>To calculate the central angle for each sector:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Determine the Fraction or Percentage<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Identify the percentage or fraction of the total that each category represents.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Use the Formula<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Convert the percentage to a fraction (if needed) and multiply by 360\u00b0.<\/li>\n\n\n\n<li><strong>Formula<\/strong>: Central Angle (in degrees) = (Percentage\/100) \u00d7 360\u00b0<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-a3e4beb69a41bd25aacd40c9b68b84b7\" style=\"color:#dc2020\"><strong>5. Steps to Create a Pie Chart with Central Angles<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Collect Data<\/strong>: Gather data and determine the percentage or fraction for each category.<\/li>\n\n\n\n<li><strong>Calculate Central Angles<\/strong>: Use the formula to calculate the central angle for each sector.<\/li>\n\n\n\n<li><strong>Draw the Circle<\/strong>: Draw a circle representing the entire dataset.<\/li>\n\n\n\n<li><strong>Draw Sectors<\/strong>: Starting from a fixed radius (like the 12 o\u2019clock position), use a protractor to measure and draw each sector\u2019s central angle.<\/li>\n\n\n\n<li><strong>Label Sectors<\/strong>: Label each sector with its category name and the corresponding percentage or fraction.<\/li>\n\n\n\n<li><strong>Add a Legend<\/strong>: Include a legend if necessary to clarify the categories.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-9bd5e05cc9ee57c0191c175699b2ac42\" style=\"color:#87bf42\"><strong>6. Interpreting Pie Charts with Central Angles<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Visualizing Proportions<\/strong>: Larger central angles correspond to larger sectors, indicating a larger proportion of the data.<\/li>\n\n\n\n<li><strong>Comparing Categories<\/strong>: By comparing the central angles or sector sizes, you can determine which categories are most or least significant<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-28b713078618ac836c57509fc680db42\" style=\"color:#a822d8\"><strong>7. Examples and Practice<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Example 1<\/strong>: A pie chart representing time spent on daily activities.\n<ul class=\"wp-block-list\">\n<li>Categories: Sleep , Schoo, Homework , Leisure , Others <\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71-1024x1024.png\" alt=\"\" class=\"wp-image-17262\" style=\"width:368px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71-1024x1024.png 1024w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71-150x150.png 150w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71-768x768.png 768w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71-400x400.png 400w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71-1536x1536.png 1536w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-71.png 1563w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-98cd8cab7668d57fe118d7c0933cfe84\" style=\"color:#43d2d2\"><strong>8. Real-World Applications<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Business<\/strong>: Pie charts with central angles are used in business to represent market share, budget allocations, and survey results.<\/li>\n\n\n\n<li><strong>Science<\/strong>: Used to visualize data distributions, such as species population, energy consumption, or resource allocation.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-6f208eba1214753aeb86b718f4e2dbc7\" style=\"color:#dc1818\"><strong>9. Common Mistakes to Avoid<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Incorrect Angle Calculation<\/strong>: Ensure accurate calculations to prevent misrepresentation of data.<\/li>\n\n\n\n<li><strong>Overlapping Sectors<\/strong>: Ensure that the sum of the central angles equals 360\u00b0 to avoid overlapping or gaps between sectors.<\/li>\n<\/ul>\n<\/div><\/div>\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:#c7edbd\"><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 has-link-color wp-elements-b38d454c1355adce32d0037c0c32eefe\" style=\"color:#b00012\">\ud83d\udd8d\ufe0f <strong>Melton&#8217;s Flooring sponsored a survey about home flooring preferences.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-4.png\" alt=\"\" class=\"wp-image-6834\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-4.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-4-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-4-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>\ud83d\udd8d\ufe0f What is the measure of the central angle in the &#8220;Vinyl&#8221; section?<\/p>\n\n\n\n<p>&#8212;&#8212;&#8211;\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>According to the graph, 15% of the respondents preferred vinyl flooring.<\/p>\n\n\n\n<p>Find 15% of 360\u00b0.<\/p>\n\n\n\n<p>15% of 360\u00b0=0.15* 360\u00b0<\/p>\n\n\n\n<p>=54\u00b0<\/p>\n\n\n\n<p>In the &#8220;Vinyl&#8221; section, the measure of the central angle is 54\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#c7f1d5\"><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 has-link-color wp-elements-33df9a6ff498f245b479f93564058aa1\" style=\"color:#b00012\">\ud83d\udd8d\ufe0f <strong>Arcadia requires all dogs to be registered with the city and keeps records of the distribution of different breeds.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-25.png\" alt=\"\" class=\"wp-image-6838\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-25.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-25-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-25-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>\ud83d\udd8d\ufe0f What is the measure of the central angle in the &#8220;Labrador Retrievers&#8221; section?<\/p>\n\n\n\n<p>&#8212;&#8212;&#8212;&#8212;&#8212;-\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>According to the graph, 30% of dogs registered with the city are Labrador Retrievers.<\/p>\n\n\n\n<p>Find 30% of 360\u00b0.<\/p>\n\n\n\n<p>30% of 360\u00b0=0.30*360\u00b0<\/p>\n\n\n\n<p>=108\u00b0<\/p>\n\n\n\n<p>In the &#8220;Labrador Retrievers&#8221; section, the measure of the central angle is 108\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#b6cef4\"><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 has-link-color wp-elements-d6f48d1f677d54f7ce1424d096622c7b\" style=\"color:#b00012\">\ud83d\udd8d\ufe0f <strong>The visitors to a certain website were interviewed about their favourite gum flavours.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-8.png\" alt=\"\" class=\"wp-image-6844\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-8.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-8-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-8-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>\ud83d\udd8d\ufe0f What is the measure of the central angle in the &#8220;Peppermint&#8221; section?<\/p>\n\n\n\n<p>&#8212;&#8212;&#8211;\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>According to the graph, 65% of people chose &#8220;Peppermint&#8221;.<\/p>\n\n\n\n<p>Find 65% of 360\u00b0.<\/p>\n\n\n\n<p>65% of 360\u00b0=0.65\u00d7 360\u00b0<\/p>\n\n\n\n<p>=234\u00b0<\/p>\n\n\n\n<p>In the &#8220;Peppermint&#8221; section, the measure of the central angle is 234\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/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\/76714\/067\/506\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-187.png\" alt=\"\" class=\"wp-image-9109\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-187.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-187-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-187-150x150.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\/76716\/476\/708\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-192.png\" alt=\"\" class=\"wp-image-9110\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-192.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-192-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-192-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pie charts and central angles Key Notes: 1. Definition of a Pie Chart 2. Components of a Pie Chart 3. Understanding Central Angles 4. Calculating Central Angles To calculate the central angle for each sector: 5. Steps to Create a Pie Chart with Central Angles 6. Interpreting Pie Charts with Central Angles 7. Examples and<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/z-14-pie-charts-and-central-angles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;Z.14 Pie charts and central angles&#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-535","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\/535","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=535"}],"version-history":[{"count":24,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/535\/revisions"}],"predecessor-version":[{"id":19938,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/535\/revisions\/19938"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}