Calculate the mean, x\u23af\u23af\u23af, and standard deviation, , for the data set.
Sample Value
1 6.016
2 6.029
3 6.026
4 6.025
5 6.018
6 6.015<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The mean ((\\bar{x})) of the given data set is 6.0215<\/strong>, and the standard deviation ((s)) is approximately 0.00589<\/strong>.<\/p>\n\n\n\n Calculate the mean, x\u23af\u23af\u23af, and standard deviation, , for the data set.Sample Value1 6.0162 6.0293 6.0264 6.0255 6.0186 6.015 The Correct Answer and Explanation is: The mean ((\\bar{x})) of the given data set is 6.0215, and the standard deviation ((s)) is approximately 0.00589. Explanation: Significance:<\/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-168717","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168717","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=168717"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168717\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
\n
The mean, also known as the arithmetic average, is calculated as the sum of all values divided by the number of values in the data set:
[
\\bar{x} = \\frac{\\sum x_i}{n}
]
Here:
[
x_1 = 6.016, \\, x_2 = 6.029, \\, x_3 = 6.026, \\, x_4 = 6.025, \\, x_5 = 6.018, \\, x_6 = 6.015
]
Summing these values gives:
[
\\sum x_i = 6.016 + 6.029 + 6.026 + 6.025 + 6.018 + 6.015 = 36.129
]
Dividing by the number of samples ((n = 6)):
[
\\bar{x} = \\frac{36.129}{6} = 6.0215
]<\/li>\n\n\n\n
The standard deviation measures the dispersion of the data from the mean. For a sample, the formula is:
[
s = \\sqrt{\\frac{\\sum (x_i – \\bar{x})^2}{n-1}}
]
Subtracting the mean from each data point gives deviations:
[
\\text{Deviations: } -0.0055, 0.0075, 0.0045, 0.0035, -0.0035, -0.0065
]
Squaring these deviations and summing them gives:
[
\\sum (x_i – \\bar{x})^2 = 0.00003025 + 0.00005625 + 0.00002025 + 0.00001225 + 0.00001225 + 0.00004225 = 0.0001735
]
Dividing by (n-1 = 5) and taking the square root:
[
s = \\sqrt{\\frac{0.0001735}{5}} = \\sqrt{0.0000347} \\approx 0.00589
]<\/li>\n<\/ol>\n\n\n\nSignificance:<\/h3>\n\n\n\n
\n