{"id":547,"date":"2022-04-13T05:30:11","date_gmt":"2022-04-13T05:30:11","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=547"},"modified":"2025-04-08T09:15:22","modified_gmt":"2025-04-08T09:15:22","slug":"aa-4-changes-in-mean-median-mode-and-range","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/aa-4-changes-in-mean-median-mode-and-range\/","title":{"rendered":"AA.4 Changes in mean, median, mode and range"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Changes in mean, median, mode and range<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-869a5c0b6b78055316c8d0186252dcbd\" style=\"color:#74008b\"><strong>key notes :<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b9d0dffe1e9f90b12b8ce7770ee6654e\" style=\"color:#000060\"><strong>Mean<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Formula<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\">The mean is the average of a set of numbers.<\/p>\n\n\n\n<p class=\"has-large-font-size\">To find the mean, add all the numbers together and divide by the total count of numbers.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"413\" height=\"84\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2025\/04\/image-10.png\" alt=\"\" class=\"wp-image-20404\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2025\/04\/image-10.png 413w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2025\/04\/image-10-300x61.png 300w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\"><strong>Changes in Mean<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>If you add or remove a number, the mean will change based on the value of the number.<\/li>\n\n\n\n<li>A large value added or removed will cause a bigger shift in the mean compared to a smaller value.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-21f905f879cb3058a6bf32526cdfbb7b\" style=\"color:#000060\"><strong>Median<\/strong>:<\/h3>\n\n\n\n<p class=\"has-large-font-size\">The median is the middle value when the data is arranged in ascending or descending order.<\/p>\n\n\n\n<p class=\"has-large-font-size\">If there\u2019s an odd number of values, the median is the middle number.<\/p>\n\n\n\n<p class=\"has-large-font-size\">If there\u2019s an even number of values, the median is the average of the two middle numbers.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Changes in Median<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Adding or removing numbers can change the position of the median.<\/li>\n\n\n\n<li>If the data set is large, changes in individual values might not affect the median unless the new values push the middle numbers.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-a1ee6d5495e569ef396c24df84f807a9\" style=\"color:#000060\"><strong>Mode<\/strong>:<\/h3>\n\n\n\n<p class=\"has-large-font-size\">The mode is the number that appears most frequently in a data set.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>A data set can have:<\/li>\n\n\n\n<li>One mode (unimodal).<\/li>\n\n\n\n<li>Two modes (bimodal).<\/li>\n\n\n\n<li>More than two modes (multimodal).<\/li>\n\n\n\n<li>No mode if no number repeats.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Changes in Mode<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>If a new number is added that already exists in the data set, the mode might remain the same or change.<\/li>\n\n\n\n<li>If a new number is added that is different from all the others, the mode might stay the same, or there might be no mode.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-21e72297119464822f8f2aad96ce4609\" style=\"color:#000060\"><strong>Range<\/strong>:<\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The range is the difference between the highest and lowest values in the data set.<\/li>\n\n\n\n<li><strong>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=\"385\" height=\"62\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2025\/04\/image-11.png\" alt=\"\" class=\"wp-image-20405\" style=\"width:431px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2025\/04\/image-11.png 385w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2025\/04\/image-11-300x48.png 300w\" sizes=\"auto, (max-width: 385px) 100vw, 385px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\"><strong>Changes in Range<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Adding a number greater than the current highest value increases the range.<\/li>\n\n\n\n<li>Adding a number smaller than the current lowest value also increases the range.<\/li>\n\n\n\n<li>Removing the highest or lowest value can decrease the range.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-715ee71bbd1a0fa3113f489579c720b0\" style=\"color:#000060\"><strong>General Impact of Changes<\/strong>:<\/h3>\n\n\n\n<p class=\"has-large-font-size\"><strong>Addition\/Removal of Numbers<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Adding numbers can shift the mean, median, and range depending on the values added.<\/li>\n\n\n\n<li>Removing numbers can also affect all measures, especially if the number removed is the highest, lowest, or middle value.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Effect of Extreme Values (Outliers)<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Outliers (extremely high or low values) can significantly affect the mean and range but have less effect on the median and mode.<\/li>\n<\/ul>\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-background has-large-font-size\" style=\"background-color:#043702\"><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-primary-color has-text-color has-link-color wp-elements-b426c6c68af4a7c9786bc61df0dab153\"><strong>Look at this set of 9 numbers:<br>2 2 7 2 1 5 2 4 3<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-99d261a7869580822a80c8a527a71bea\" style=\"color:#d90000\">How would the range change if the number 2 replaced the number 7 in the set?<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-a3cd190704bf07fa60a08d7849a9f091\"><strong>increase      decrease      no change<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-abaa139bd251f4146935e09c10ff859f\">Find the original range. Subtract the least number from the greatest number<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-41dbb5f517ac490c5b7679b6030ea0bd\">7-1=6<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-5282703a1e066ed4903541673adc9324\">The original range is 6.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c458aa4aaa4e1c22e7deccb146fb689c\">Now replace 7 with 2.<br><strong>2 2 2 2 1 5 2 4 3<br><\/strong>Find the new range. Subtract the least number from the greatest number.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-fb2ef8405d4aff6a32ddc5db3ec9343a\">5-1=4<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-291d2026659306f3e4bfd2c5d37daab4\">The new range would be 4.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-f164d3234c7d95addcfea7c45df966dd\">The range would decrease from 6 to 4.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#360231\"><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-primary-color has-text-color has-link-color wp-elements-647f940944782e229ee6639b3eb1b0cd\"><strong>Look at this set of 7 numbers:<br>88 39 96 90 37 54 96<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-da1dbc79a7aa253eed7be15985bffdee\" style=\"color:#d90000\">How would the range change if the number 53 replaced the number 54 in the set?<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-1ed1ce611fbbaa551dc8b091e8752271\"><strong>increase      decrease    no change<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-39d56e5120621c174f6ed82dffda6de2\">You can solve this problem without doing any calculations. The least number in the set is 37. The greatest number is 96. Since 54 and 53 are both between 37 and 96, replacing 54 with 53 will not change the range.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-bbd954785f9b2ae1430de5b5361ba9d0\">You can check your answer by doing the calculations.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-480016deed0402ec6629e1378bfe00c3\">Find the original range. Subtract the least number from the greatest number.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-0d8279235155498b80a2775d7f7887be\">96-37=59<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-8b4d41f24c9af534cc214c9980a83734\">The original range is 59.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-971988be5c84a7d96afa3b2eb39d1b1c\">Now replace 54 with 53.<br>8839969037<strong>53<\/strong>96<br>Find the new range. Subtract the least number from the greatest number.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-0d8279235155498b80a2775d7f7887be\">96-37=59<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-46cf2c95ca185dfccc3f73dd5366e1aa\">The new range would also be 59.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c92d65cb14db18e173a724d5244014f2\">The range would not change.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#02313d\"><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-primary-color has-text-color has-link-color wp-elements-b7f813551d86a28afce644d0a44e9d59\"><strong>Look at this set of 7 numbers:<br>4 6 3 4 7 2 9<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-516d068ee5b20946c5e5444fe605cfc0\" style=\"color:#d90000\">How would the range change if the number 4 replaced the number 6 in the set?<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-a0547af55221305ee9cbf4f13c3714ef\"><strong>increase        decrease     no change<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-9e39f63e9764565379f3a059510e3bb4\">You can solve this problem without doing any calculations. The least number in the set is 2. The greatest number is 9. Since 6 and 4 are both between 2 and 9, replacing 6 with 4 will not change the range.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-bbd954785f9b2ae1430de5b5361ba9d0\">You can check your answer by doing the calculations.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-480016deed0402ec6629e1378bfe00c3\">Find the original range. Subtract the least number from the greatest number.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-58e16771e17d5205a9ded107136b3d95\">9-2=7<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-66497c5af1d66a029189756acec1c02d\">The original range is 7.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-f106f0c77415ae36df28fda1a734c0b2\">Now replace 6 with 4.<br>4<strong>4<\/strong>34729<br>Find the new range. Subtract the least number from the greatest number.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-58e16771e17d5205a9ded107136b3d95\">9-2=7<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-7c7d4054d1bfdf1c2fc11a655d32feca\">The new range would also be 7.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c92d65cb14db18e173a724d5244014f2\">The range would not change.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>let&#8217;s practice!<\/strong><\/p>\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\/75551\/369\/591\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-198.png\" alt=\"\" class=\"wp-image-9147\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-198.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-198-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-198-150x150.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\/89993\/887\/286\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-204.png\" alt=\"\" class=\"wp-image-9148\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-204.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-204-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-204-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Changes in mean, median, mode and range key notes : Mean: Formula: The mean is the average of a set of numbers. To find the mean, add all the numbers together and divide by the total count of numbers. Changes in Mean: Median: The median is the middle value when the data is arranged in<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/aa-4-changes-in-mean-median-mode-and-range\/\">Continue reading <span class=\"screen-reader-text\">&#8220;AA.4 Changes in mean, median, mode and range&#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-547","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\/547","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=547"}],"version-history":[{"count":22,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/547\/revisions"}],"predecessor-version":[{"id":20426,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/547\/revisions\/20426"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}