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?

Question

Options

• A147mm
• B154mm
• C394mm
• D21,704mm

• A
  7% (4)
• B
  78% (42)
• C
  11% (6)
• D
  4% (2)

Explanation

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 + 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.

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