find the mean variance and standard deviation for the data set
4 13 9 2 10 7 15 5 17 18
the mean is x =__
round 2 decimal places
To find the mean, variance, and standard deviation for the given data set, we first need to calculate the mean:
Mean (x) = (4 + 13 + 9 + 2 + 10 + 7 + 15 + 5 + 17 + 18) / 10
Mean (x) = 100 / 10
Mean (x) = 10
Next, we calculate the variance:
Variance = [(4-10)^2 + (13-10)^2 + (9-10)^2 + (2-10)^2 + (10-10)^2 + (7-10)^2 + (15-10)^2 + (5-10)^2 + (17-10)^2 + (18-10)^2] / 10
Variance = [(-6)^2 + 3^2 + (-1)^2 + (-8)^2 + 0^2 + (-3)^2 + 5^2 + (-5)^2 + 7^2 + 8^2] / 10
Variance = [36 + 9 + 1 + 64 + 0 + 9 + 25 + 25 + 49 + 64] / 10
Variance = 282 / 10
Variance = 28.2
Lastly, we calculate the standard deviation:
Standard Deviation = √28.2
Standard Deviation ≈ 5.313
Therefore, the mean (x) is 10, the variance is 28.2, and the standard deviation is approximately 5.313.