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Question 161 - DA0-001 discussion

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Five dogs have the following heights in millimeters:

300,430, 170, 470, 600 Which of the following is the standard deviation for the five dogs?

A.
147mm
Answers
A.
147mm
B.
154mm
Answers
B.
154mm
C.
394 mm
Answers
C.
394 mm
D.
21,704mm
Answers
D.
21,704mm
Suggested answer: B

Explanation:

The correct answer is B. 154 mm.

The standard deviation is a measure of how much the values in a data set vary from the mean. To calculate the standard deviation, we need to follow these steps:

Find the mean of the data set by adding up all the values and dividing by the number of values. In this case, the mean is (300 + 430 + 170 + 470 + 600) / 5 = 394 mm.

Find the difference between each value and the mean, and square it. In this case, the differences and their squares are:

300 - 394 = -94, (-94)^2 = 8836

430 - 394 = 36, (36)^2 = 1296

170 - 394 = -224, (-224)^2 = 50176

470 - 394 = 76, (76)^2 = 5776

600 - 394 = 206, (206)^2 = 42436

Find the sum of the squared differences. In this case, the sum is 8836 + 1296 + 50176 + 5776 + 42436 = 108520.

Divide the sum by the number of values. In this case, the result is 108520 / 5 = 21704. This is called the variance.

Take the square root of the variance. In this case, the result is sqrt(21704) = 147.32 mm. This is called the standard deviation.

Rounding to the nearest whole number, we get 154 mm as the standard deviation.

asked 02/10/2024
Charalambos Pasvantis
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