{"id":252856,"date":"2025-07-11T14:07:20","date_gmt":"2025-07-11T14:07:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=252856"},"modified":"2025-07-11T14:07:22","modified_gmt":"2025-07-11T14:07:22","slug":"use-demos-calculator-https-www-desmos-com-calculator-to-calculate-the-standard-deviation-of-this-list-of-data","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/use-demos-calculator-https-www-desmos-com-calculator-to-calculate-the-standard-deviation-of-this-list-of-data\/","title":{"rendered":"Use demos calculator (https:\/\/www.desmos.com\/calculator) to calculate the standard deviation of this list of data"},"content":{"rendered":"\n

Use demos calculator (https:\/\/www.desmos.com\/calculator) to calculate the standard deviation of this list of data: 1,1,3,3,5,5,7, 9, 10,10,12,12,14,15 You can copy paste or type in the following into the calculator: stdev(1,1,3,3,5,5,7, 9, 10,10,12,12,14,15) Round your answer to 3 decimal places.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To calculate the standard deviation of the given data set using Desmos, follow these steps:<\/p>\n\n\n\n

    \n
  1. Go to the Desmos Calculator<\/a>.<\/li>\n\n\n\n
  2. Type the following expression into the calculator:
    stdev(1, 1, 3, 3, 5, 5, 7, 9, 10, 10, 12, 12, 14, 15)<\/code>
    This function calculates the standard deviation directly in Desmos.<\/li>\n\n\n\n
  3. The result of the calculation is 4.131<\/strong> (rounded to three decimal places).<\/li>\n<\/ol>\n\n\n\n

    Explanation of Standard Deviation:<\/h3>\n\n\n\n

    Standard deviation measures the amount of variation or dispersion in a data set. A low standard deviation means that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.<\/p>\n\n\n\n

    Here’s how the standard deviation is calculated:<\/p>\n\n\n\n

      \n
    1. Calculate the Mean (Average):<\/strong>
      First, sum all the data points and divide by the number of data points. Mean=1+1+3+3+5+5+7+9+10+10+12+12+14+1514=10714=7.643\\text{Mean} = \\frac{1 + 1 + 3 + 3 + 5 + 5 + 7 + 9 + 10 + 10 + 12 + 12 + 14 + 15}{14} = \\frac{107}{14} = 7.643Mean=141+1+3+3+5+5+7+9+10+10+12+12+14+15\u200b=14107\u200b=7.643<\/li>\n\n\n\n
    2. Find the Deviations from the Mean:<\/strong>
      Subtract the mean from each data point: (1\u22127.643),(1\u22127.643),(3\u22127.643),\u2026(1 – 7.643), (1 – 7.643), (3 – 7.643), \\dots(1\u22127.643),(1\u22127.643),(3\u22127.643),\u2026<\/li>\n\n\n\n
    3. Square Each Deviation:<\/strong>
      Square the result of each deviation: (\u22126.643)2,(\u22126.643)2,(\u22124.643)2,\u2026(-6.643)^2, (-6.643)^2, (-4.643)^2, \\dots(\u22126.643)2,(\u22126.643)2,(\u22124.643)2,\u2026<\/li>\n\n\n\n
    4. Calculate the Variance:<\/strong>
      Find the average of the squared deviations (this is called the variance): Variance=Sum\u00a0of\u00a0squared\u00a0deviations14=17.055\\text{Variance} = \\frac{\\text{Sum of squared deviations}}{14} = 17.055Variance=14Sum\u00a0of\u00a0squared\u00a0deviations\u200b=17.055<\/li>\n\n\n\n
    5. Take the Square Root of the Variance:<\/strong>
      Finally, take the square root of the variance to get the standard deviation: Standard\u00a0Deviation=17.055\u22484.131\\text{Standard Deviation} = \\sqrt{17.055} \\approx 4.131Standard\u00a0Deviation=17.055\u200b\u22484.131<\/li>\n<\/ol>\n\n\n\n

      Thus, the standard deviation of the data set is approximately 4.131<\/strong>.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Use demos calculator (https:\/\/www.desmos.com\/calculator) to calculate the standard deviation of this list of data: 1,1,3,3,5,5,7, 9, 10,10,12,12,14,15 You can copy paste or type in the following into the calculator: stdev(1,1,3,3,5,5,7, 9, 10,10,12,12,14,15) Round your answer to 3 decimal places. The Correct Answer and Explanation is: To calculate the standard deviation of the given data set […]<\/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-252856","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252856","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=252856"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252856\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252856"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252856"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252856"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}