Find the mean, variance, and standard deviation for the following data set. Round to the nearest tenth.
55, 87, 62, 85, 93, 75
Mean:
(55 + 87 + 62 + 85 + 93 + 75) / 6 = 457 / 6 = 76.2
Variance:
Step 1: Calculate the mean (76.2)
Step 2: Subtract the mean from each data point and square the result:
(55 - 76.2)^2 = 441.64
(87 - 76.2)^2 = 115.24
(62 - 76.2)^2 = 200.04
(85 - 76.2)^2 = 77.44
(93 - 76.2)^2 = 281.64
(75 - 76.2)^2 = 14.44
Step 3: Add up all the squared differences:
441.64 + 115.24 + 200.04 + 77.44 + 281.64 + 14.44 = 1130.44
Step 4: Divide the result by the number of data points minus 1 (6 - 1 = 5):
1130.44 / 5 = 226.088
Variance = 226.1
Standard Deviation:
Standard deviation = √variance
Standard deviation = √226.1
Standard deviation ≈ 15.0
Therefore, the mean is 76.2, the variance is 226.1, and the standard deviation is approximately 15.0.