Calculate, correct to one decimal place, the standard deviation of the numbers: -1, 5, 0, 2 and 9.
Question 1 Report
Calculate, correct to one decimal place, the standard deviation of the numbers: -1, 5, 0, 2 and 9.
Answer Details
To find the standard deviation of a set of numbers, we need to first calculate the mean of the numbers, then subtract the mean from each number to get the deviations, square each deviation, find the mean of the squared deviations (variance), and finally take the square root of the variance to get the standard deviation.
So first, let's find the mean:
mean = (-1 + 5 + 0 + 2 + 9) / 5 = 3
Next, we'll find the deviations by subtracting the mean from each number:
-1 - 3 = -4
5 - 3 = 2
0 - 3 = -3
2 - 3 = -1
9 - 3 = 6
Now we'll square each deviation:
(-4)^2 = 16
2^2 = 4
(-3)^2 = 9
(-1)^2 = 1
6^2 = 36
Next, we'll find the mean of the squared deviations:
(16 + 4 + 9 + 1 + 36) / 5 = 13.2
Finally, we'll take the square root of the variance to get the standard deviation:
sqrt(13.2) ≈ 3.6
So the answer is (c) 3.6, correct to one decimal place.
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