{"id":34,"date":"2022-05-20T16:59:03","date_gmt":"2022-05-20T16:59:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-variability-of-data-sets-what-to-know-5\/"},"modified":"2022-06-16T15:21:23","modified_gmt":"2022-06-16T15:21:23","slug":"comparing-variability-of-data-sets-what-to-know-4-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-variability-of-data-sets-what-to-know-4-2\/","title":{"raw":"Comparing Variability of Data Sets: Learn It 4","rendered":"Comparing Variability of Data Sets: Learn It 4"},"content":{"raw":"

Variance<\/h2>\r\n
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Variance<\/h3>\r\n\r\n
\r\n

the standard deviation squared, [latex]\\sigma^{2}[\/latex] or\u00a0[latex]s^{2}[\/latex]<\/p>\r\n \r\n

Variance of a population<\/strong>:\u00a0 [latex]\\sigma^{2}=\\dfrac{\\sum\\left(x-\\mu\\right)^{2}}{n}[\/latex]<\/p>\r\n

Variance of a sample<\/strong>:\u00a0 [latex]s^{2}=\\dfrac{\\sum\\left(x-\\bar{x}\\right)^{2}}{n-1}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

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Try it 6<\/h3>\r\n
\"\"<\/div>\r\nImportant<\/em>: The statistical technology tool does not calculate variance, so you will need to use the tool to calculate the standard deviation and then square it by hand in order to get the variance.[ohm_question hide_question_numbers=1]241061[\/ohm_question]\r\n\r\n[reveal-answer q=\"280916\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"280916\"]First identify the standard deviation using the statistical technology tool, then square that value by hand. Round to\u00a0[latex]3[\/latex] decimal places.[\/hidden-answer]\r\n\r\n<\/div>\r\n

Range<\/h2>\r\n
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Range<\/h3>\r\n\r\n
\r\n

maximum value \u2013 minimum value<\/p>\r\n

or<\/p>\r\n

largest value \u2013 smallest value<\/p>\r\n\r\n<\/div>\r\nWhen the range is larger, it indicates more variability in the data. However, range only utilizes two observations in the entire data set to measure variability, so it is not an ideal measure of spread when used alone. But when used in combination with other measures of variance, it can help us gain a clearer understanding of the spread of a distribution.\r\n

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Try it 7<\/h3>\r\n
\"\"<\/div>\r\n[ohm_question hide_question_numbers=1]241062[\/ohm_question]\r\n\r\n[reveal-answer q=\"236844\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"236844\"]Look for \u201cMax.\u201d and \u201cMin.\u201d in the summary of descriptive statistics within the statistical technology tool.[\/hidden-answer]\r\n\r\n<\/div>","rendered":"

Variance<\/h2>\n
\n

Variance<\/h3>\n
\n

the standard deviation squared, [latex]\\sigma^{2}[\/latex] or\u00a0[latex]s^{2}[\/latex]<\/p>\n

 <\/p>\n

Variance of a population<\/strong>:\u00a0 [latex]\\sigma^{2}=\\dfrac{\\sum\\left(x-\\mu\\right)^{2}}{n}[\/latex]<\/p>\n

Variance of a sample<\/strong>:\u00a0 [latex]s^{2}=\\dfrac{\\sum\\left(x-\\bar{x}\\right)^{2}}{n-1}[\/latex]<\/p>\n<\/div>\n

\n

Try it 6<\/h3>\n
\"\"<\/div>\n

Important<\/em>: The statistical technology tool does not calculate variance, so you will need to use the tool to calculate the standard deviation and then square it by hand in order to get the variance.