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For the following set of data, find the sample standard deviation, to the nearest hundredth. $\newline$ $146,147,144,117,105,105,89$

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Find the magnitude and direction of a vector sum

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Q. For the following set of data, find the sample standard deviation, to the nearest hundredth.

\newline

146,147,144,117,105,105,89

List and Verify Data: List the data set and verify the numbers. $\newline$ Data set: $146, 147, 144, 117, 105, 105, 89$ $\newline$ Check for any input errors in the data set.
Calculate Mean: Calculate the mean (average) of the data set. $\newline$ Mean = $(146 + 147 + 144 + 117 + 105 + 105 + 89) / 7$ $\newline$ Mean = $853 / 7$ $\newline$ Mean = $121.8571$ (rounded to four decimal places for accuracy in further calculations)
Square and Subtract: Subtract the mean from each data point and square the result. $\newline$ $(146 - 121.8571)^2 = 583.2659$ $\newline$ $(147 - 121.8571)^2 = 631.2659$ $\newline$ $(144 - 121.8571)^2 = 491.2659$ $\newline$ $(117 - 121.8571)^2 = 23.5914$ $\newline$ $(105 - 121.8571)^2 = 283.5914$ $\newline$ $(105 - 121.8571)^2 = 283.5914$ $\newline$ $(89 - 121.8571)^2 = 1078.5914$
Sum Squared Differences: Sum the squared differences. $\newline$ Sum = $583.2659 + 631.2659 + 491.2659 + 23.5914 + 283.5914 + 283.5914 + 1078.5914$ $\newline$ Sum = $3374.1633$
Calculate Variance: Divide the sum of the squared differences by the sample size minus one to get the variance. $\newline$ Sample size $n$ = $7$ $\newline$ Variance = $\text{Sum} / (n - 1)$ $\newline$ Variance = $3374.1633 / (7 - 1)$ $\newline$ Variance = $3374.1633 / 6$ $\newline$ Variance = $562.3606$
Calculate Standard Deviation: Take the square root of the variance to get the sample standard deviation. $\newline$ Standard deviation = $\sqrt{562.3606}$ $\newline$ Standard deviation = $23.7159$
Round Standard Deviation: Round the standard deviation to the nearest hundredth. $\newline$ Standard deviation (rounded) = $23.72$

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