{"id":144363,"date":"2024-09-24T14:30:20","date_gmt":"2024-09-24T14:30:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=144363"},"modified":"2024-09-24T14:30:22","modified_gmt":"2024-09-24T14:30:22","slug":"here-are-ten-numbers","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/24\/here-are-ten-numbers\/","title":{"rendered":"Here are ten numbers"},"content":{"rendered":"\n<p>Here are ten numbers<br>3 ,7,2,4,7,5,7,1,8,8<br>(a) write down the mode<br>(b) Work out the median<br>(c) Calculate the mean<br>(d) What is the range ?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let\u2019s analyze the given set of numbers: 3, 7, 2, 4, 7, 5, 7, 1, 8, 8. We will calculate the mode, median, mean, and range of these numbers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(a) Mode<\/h3>\n\n\n\n<p>The mode is the number that appears most frequently in a data set. In our case, we have:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1<\/strong>: appears 1 time<\/li>\n\n\n\n<li><strong>2<\/strong>: appears 1 time<\/li>\n\n\n\n<li><strong>3<\/strong>: appears 1 time<\/li>\n\n\n\n<li><strong>4<\/strong>: appears 1 time<\/li>\n\n\n\n<li><strong>5<\/strong>: appears 1 time<\/li>\n\n\n\n<li><strong>7<\/strong>: appears 3 times<\/li>\n\n\n\n<li><strong>8<\/strong>: appears 2 times<\/li>\n<\/ul>\n\n\n\n<p>The mode of this set is <strong>7<\/strong>, as it occurs most frequently.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(b) Median<\/h3>\n\n\n\n<p>To find the median, we need to arrange the numbers in ascending order:<\/p>\n\n\n\n<p><strong>1, 2, 3, 4, 5, 7, 7, 7, 8, 8<\/strong><\/p>\n\n\n\n<p>Since there are 10 numbers (an even count), the median will be the average of the two middle numbers, which are the 5th and 6th numbers in this ordered list.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The 5th number is <strong>5<\/strong>.<\/li>\n\n\n\n<li>The 6th number is <strong>7<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>To find the median, we calculate the average of these two numbers:<\/p>\n\n\n\n<p>[<br>\\text{Median} = \\frac{5 + 7}{2} = \\frac{12}{2} = 6<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(c) Mean<\/h3>\n\n\n\n<p>The mean is calculated by summing all the numbers and dividing by the count of the numbers:<\/p>\n\n\n\n<p>[<br>\\text{Sum} = 3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8 = 52<br>]<\/p>\n\n\n\n<p>The count of the numbers is <strong>10<\/strong>. Thus, the mean is:<\/p>\n\n\n\n<p>[<br>\\text{Mean} = \\frac{52}{10} = 5.2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(d) Range<\/h3>\n\n\n\n<p>The range is determined by subtracting the smallest number from the largest number in the set.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The smallest number is <strong>1<\/strong>.<\/li>\n\n\n\n<li>The largest number is <strong>8<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the range is calculated as follows:<\/p>\n\n\n\n<p>[<br>\\text{Range} = 8 &#8211; 1 = 7<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary of Results<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mode<\/strong>: 7<\/li>\n\n\n\n<li><strong>Median<\/strong>: 6<\/li>\n\n\n\n<li><strong>Mean<\/strong>: 5.2<\/li>\n\n\n\n<li><strong>Range<\/strong>: 7<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of Statistical Concepts<\/h3>\n\n\n\n<p>Understanding these basic statistics is crucial for interpreting data effectively. The <strong>mode<\/strong> gives insight into the most common value, useful in identifying trends or preferences within a dataset. The <strong>median<\/strong> provides a measure of central tendency that is not affected by extreme values (outliers), making it a reliable measure in skewed distributions. The <strong>mean<\/strong>, however, considers all values and can be influenced by outliers, providing a more comprehensive view of the average. Lastly, the <strong>range<\/strong> highlights the spread of the data, indicating the extent of variability. Each of these measures offers unique insights, and together they help to form a complete picture of the data set\u2019s characteristics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here are ten numbers3 ,7,2,4,7,5,7,1,8,8(a) write down the mode(b) Work out the median(c) Calculate the mean(d) What is the range ? The Correct answer and Explanation is: Let\u2019s analyze the given set of numbers: 3, 7, 2, 4, 7, 5, 7, 1, 8, 8. We will calculate the mode, median, mean, and range of these [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-144363","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=144363"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144363\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}