{"id":196374,"date":"2025-03-04T19:24:25","date_gmt":"2025-03-04T19:24:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196374"},"modified":"2025-03-04T19:24:28","modified_gmt":"2025-03-04T19:24:28","slug":"creating-a-histogram-by-super-imposing-a-normal-distribution-h-histogram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/04\/creating-a-histogram-by-super-imposing-a-normal-distribution-h-histogram\/","title":{"rendered":"Creating a histogram by super imposing a normal distribution \u00a0 h = histogram"},"content":{"rendered":"\n

Creating a histogram by super imposing a normal distribution \u00a0 h = histogram(data,’Normalization’,’probability’);

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

A histogram<\/strong> is a graphical representation that organizes a set of data points into user-specified ranges. In this case, we use MATLAB-style syntax:<\/p>\n\n\n\n

h = histogram(data,'Normalization','probability');\n<\/code><\/pre>\n\n\n\n
This command creates a histogram where the y-axis represents probability density<\/strong>, meaning the area under the bars sums to 1.<\/p>\n\n\n\n
However, in Python, the equivalent command is:<\/p>\n\n\n\n
plt.hist(data, bins=30, density=True, alpha=0.6, color='blue', edgecolor='black')\n<\/code><\/pre>\n\n\n\n
This ensures that the histogram is normalized<\/strong> so it can be directly compared to a probability density function (PDF).<\/p>\n\n\n\n
Superimposing a Normal Distribution<\/strong><\/h3>\n\n\n\n
To compare the data distribution to a theoretical normal distribution, we:<\/p>\n\n\n\n
    \n
  1. Compute the mean (mu<\/code>) and standard deviation (std<\/code>)<\/strong> of the dataset.<\/li>\n\n\n\n
  2. Generate values for the normal distribution<\/strong> using scipy.stats.norm.pdf<\/code>, which provides the probability density function (PDF).<\/li>\n\n\n\n
  3. Plot the normal distribution curve<\/strong> over the histogram.<\/li>\n<\/ol>\n\n\n\n
    The equation for the normal distribution PDF is: f(x)=1\u03c32\u03c0e\u2212(x\u2212\u03bc)22\u03c32f(x) = \\frac{1}{\\sigma \\sqrt{2\\pi}} e^{-\\frac{(x – \\mu)^2}{2\\sigma^2}}<\/p>\n\n\n\n
    Where:<\/p>\n\n\n\n
      \n
    • \u03bc\\mu (mu) is the mean.<\/li>\n\n\n\n
    • \u03c3\\sigma (sigma) is the standard deviation.<\/li>\n<\/ul>\n\n\n\n
      Interpretation<\/strong><\/h3>\n\n\n\n
        \n
      • If the histogram closely follows the red normal curve, the dataset is approximately normal.<\/li>\n\n\n\n
      • Deviations from the curve suggest skewness, outliers, or a different distribution.<\/li>\n<\/ul>\n\n\n\n
        This technique is widely used in statistical analysis<\/strong> to check normality before applying parametric tests like t-tests or ANOVA<\/strong>.<\/p>\n\n\n\n
        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
        Creating a histogram by super imposing a normal distribution \u00a0 h = histogram(data,’Normalization’,’probability’); The correct answer and explanation is: Explanation: A histogram is a graphical representation that organizes a set of data points into user-specified ranges. In this case, we use MATLAB-style syntax: This command creates a histogram where the y-axis represents probability density, meaning […]<\/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-196374","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196374","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=196374"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196374\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}