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 get154 mmas the standard deviation.
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