{"id":197746,"date":"2025-03-07T15:22:04","date_gmt":"2025-03-07T15:22:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=197746"},"modified":"2025-03-07T15:22:06","modified_gmt":"2025-03-07T15:22:06","slug":"if-one-project-has-a-higher-standard-deviation-than-another","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/07\/if-one-project-has-a-higher-standard-deviation-than-another\/","title":{"rendered":"If one project has a higher standard deviation than another"},"content":{"rendered":"\n<p>If one project has a higher standard deviation than another<br>a it has a higher expected value<br>b it has more possible outcomes<\/p>\n\n\n\n<p>c it has a greater risk<br>d it may be riskker, but this can only be determined by the coefficient of variation<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is **d) it may be riskier, but this can only be determined by the coefficient of variation.**<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>In project evaluation, <strong>standard deviation<\/strong> measures the <strong>absolute variability<\/strong> of a project&#8217;s returns or outcomes around its expected value (mean). A higher standard deviation indicates that the project&#8217;s returns are more spread out, suggesting greater uncertainty or risk. However, standard deviation alone doesn&#8217;t provide a complete picture of risk, especially when comparing projects with different expected values.<\/p>\n\n\n\n<p>To assess and compare the <strong>relative risk<\/strong> of projects, the <strong>coefficient of variation (CV)<\/strong> is used. The CV is calculated by dividing the standard deviation by the expected value (mean):<\/p>\n\n\n\n<p>**Coefficient of Variation (CV) = (Standard Deviation \/ Expected Value) \u00d7 100%**<\/p>\n\n\n\n<p>The CV expresses risk as a percentage of the expected value, allowing for a standardized comparison between projects with varying scales of expected returns. A higher CV indicates a higher level of risk relative to the expected return.\ue206<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>Consider two projects:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Project A:<\/strong> Expected return = $100, Standard deviation = $20<\/li>\n\n\n\n<li><strong>Project B:<\/strong> Expected return = $200, Standard deviation = $50<\/li>\n<\/ul>\n\n\n\n<p>Calculating the CV for each:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Project A:<\/strong> CV = ($20 \/ $100) \u00d7 100% = 20%<\/li>\n\n\n\n<li><strong>Project B:<\/strong> CV = ($50 \/ $200) \u00d7 100% = 25%<\/li>\n<\/ul>\n\n\n\n<p>Despite Project B having a higher standard deviation, Project A has a lower CV, indicating that Project A&#8217;s risk is smaller relative to its expected return compared to Project B.\ue206<\/p>\n\n\n\n<p>Therefore, while a higher standard deviation suggests greater variability and potential risk, the <strong>coefficient of variation<\/strong> provides a more accurate measure to determine which project is riskier relative to its expected return.\ue206<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If one project has a higher standard deviation than anothera it has a higher expected valueb it has more possible outcomes c it has a greater riskd it may be riskker, but this can only be determined by the coefficient of variation The correct answer and explanation is : The correct answer is **d) it 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