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(D) Watch Video $\newline$ Show Examples $\newline$ Question $\newline$ For the following set of data, find the population standard deviation, to the nearest hundredth. $\newline$ $139, 126, 51, 61, 77, 109, 112$ $\newline$ Copy Values for Calculator $\newline$ Open Statistics Calculator $\newline$ Answer Attempt $4$ out of $20$ $\newline$ Submit Answer $\newline$ Still Stuck?

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Find values of normal variables

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Q. (D) Watch Video

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Show Examples

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Question

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

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139, 126, 51, 61, 77, 109, 112

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Copy Values for Calculator

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Open Statistics Calculator

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Answer Attempt

4

out of

20

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Submit Answer

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Still Stuck?

List data set & calculate mean: List the data set and calculate the mean (average). $\newline$ The data set is: $139, 126, 51, 61, 77, 109, 112$ . $\newline$ To calculate the mean, sum all the values and divide by the number of values. $\newline$ Mean = $(139 + 126 + 51 + 61 + 77 + 109 + 112) / 7$ $\newline$ Mean = $675 / 7$ $\newline$ Mean $\approx 96.43$
Subtract mean & square: Subtract the mean from each data value and square the result. $\newline$ This step involves calculating the squared differences from the mean for each data point. $\newline$ $(139 - 96.43)^2 = 42.57^2 \approx 1812.2049$ $\newline$ $(126 - 96.43)^2 = 29.57^2 \approx 874.6849$ $\newline$ $(51 - 96.43)^2 = -45.43^2 \approx 2063.8849$ $\newline$ $(61 - 96.43)^2 = -35.43^2 \approx 1255.2849$ $\newline$ $(77 - 96.43)^2 = -19.43^2 \approx 377.5049$ $\newline$ $(109 - 96.43)^2 = 12.57^2 \approx 158.0849$ $\newline$ $(112 - 96.43)^2 = 15.57^2 \approx 242.5249$
Sum squared differences: Sum the squared differences. $\newline$ Sum = $1812.2049 + 874.6849 + 2063.8849 + 1255.2849 + 377.5049 + 158.0849 + 242.5249$ $\newline$ Sum $\approx 7784.1743$
Divide by data values: Divide the sum of squared differences by the number of data values to find the variance. $\newline$ Since we are calculating the population standard deviation, we divide by the total number of data points, which is $7$ . $\newline$ Variance $= 7784.1743 / 7$ $\newline$ Variance $hickapprox 1112.0249$
Find standard deviation: Take the square root of the variance to find the population standard deviation. $\newline$ Standard Deviation = $\sqrt{1112.0249}$ $\newline$ Standard Deviation $\approx 33.35$

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