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standard deviation from $4$ , $7$ , $6$ , $9$ , $4$ , $6$

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Mean, median, mode, and range

Full solution

Q. standard deviation from

4

,

7

,

6

,

9

,

4

,

6

Calculate Mean: Calculate the mean (average) of the data set. $\newline$ Mean = $(4 + 7 + 6 + 9 + 4 + 6) / 6$ $\newline$ Mean = $36 / 6$ $\newline$ Mean = $6$
Square Differences: Subtract the mean from each data point and square the result. $\newline$ $(4 - 6)^2 = (-2)^2 = 4$ $\newline$ $(7 - 6)^2 = (1)^2 = 1$ $\newline$ $(6 - 6)^2 = (0)^2 = 0$ $\newline$ $(9 - 6)^2 = (3)^2 = 9$ $\newline$ $(4 - 6)^2 = (-2)^2 = 4$ $\newline$ $(6 - 6)^2 = (0)^2 = 0$
Add Squares: Add up all the squared differences. $\newline$ Sum of squares = $4 + 1 + 0 + 9 + 4 + 0$ $\newline$ Sum of squares = $18$
Calculate Variance: Divide the sum of squares by the number of data points minus one to get the variance. $\newline$ Variance = $\frac{\text{Sum of squares}}{n - 1}$ $\newline$ Variance = $\frac{18}{6 - 1}$ $\newline$ Variance = $\frac{18}{5}$ $\newline$ Variance = $3.6$
Calculate Standard Deviation: Take the square root of the variance to get the standard deviation. $\newline$ Standard deviation = $\sqrt{\text{Variance}}$ $\newline$ Standard deviation = $\sqrt{3.6}$ $\newline$ Standard deviation = $1.897$

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