Problem 45779. Variance computation (★★★)

Created by Anirban Pal

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 198.433px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 99.2167px; transform-origin: 407px 99.2167px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 267.3px 10.5px; transform-origin: 267.3px 10.5px; unicode-bidi: normal; "><span style="">Given a vector x with several values, compute the variance, whose formula is given by:</span></span></div><div style="block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: center; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/gif;base64,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" data-image-state="image-loaded"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 283.683px 10.5px; transform-origin: 283.683px 10.5px; unicode-bidi: normal; "><span style="">where x1, x2, ...., xn are the n elements of the vector x, and μ is the average of the vector x.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.9083px 10.5px; transform-origin: 45.9083px 10.5px; unicode-bidi: normal; "><span style="">For example, if</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 109.633px 8.5px; transform-origin: 109.633px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">x = [-1, 3, 5, -4, 10, 12]</span></span></div></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.342px 10.5px; transform-origin: 256.342px 10.5px; unicode-bidi: normal; "><span style="">Then μ=4.16667 the variance is 38.16667. The following commands are forbidden:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 10.5px; transform-origin: 1.95px 10.5px; unicode-bidi: normal; "><span style=""> </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.7917px 10.5px; transform-origin: 80.7917px 10.5px; unicode-bidi: normal; "><span style="font-weight: 700; ">std, var, mean, for, while</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 10.5px; transform-origin: 1.95px 10.5px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

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Problem 45779. Variance computation (★★★)

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Problem 45779. Variance computation (★★★)

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