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1. Recall that for a sample consisting of n numbers, the standard deviation is given by s = sqrt{frac{sum_{i=1}^{n}(x_i - ar{x})^2}{n - 1}} where ar{x} is the sample mean. From this formula, derive the equivalent formula: s = sqrt{frac{n sum_{i=1}^{n} x_i^2 - (sum_{i=1}^{n} x_i)^2}{n(n - 1)}} (Hint: You may wish to work with the variance instead of the standard deviation.)

          1. Recall that for a sample consisting of n numbers, the standard deviation is given by s = sqrt{frac{sum_{i=1}^{n}(x_i - ar{x})^2}{n - 1}} where ar{x} is the sample mean. From this formula, derive the equivalent formula: s = sqrt{frac{n sum_{i=1}^{n} x_i^2 - (sum_{i=1}^{n} x_i)^2}{n(n - 1)}} (Hint: You may wish to work with the variance instead of the standard deviation.)

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$1. Recall that for a sample consisting of n numbers, the standard deviation is given by s = sqrtfracsumi=1^n(xi - arx)^2n - 1 where arx is the sample mean. From this formula, derive the equivalent formula: s = sqrtfracn sumi=1^n xi^2 - (sumi=1^n xi)^2n(n - 1) (Hint: You may wish to work with the variance instead of the standard deviation.)$

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sri K

10/06/2023

Step 1

The formula for the variance of a sample is: $$s^2 = \frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n-1}$$ where $s^2$ is the variance, $x_i$ are the individual data points, $\bar{x}$ is the sample mean, and $n$ is the number of data points. Now, let's expand the term Show more…

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Recall that for a sample consisting of n numbers, the standard deviation is given by where x is the sample mean. From this formula, derive the equivalent formula: (Hint: You may wish to work with the variance instead of the standard deviation.)

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