Find the mean, variance, and standard deviation for the following data set. Round to the nearest tenth. 55, 87, 62, 85, 93, 75 (1 point) Responses mean = 76.2 variance = 188.1 standard deviation = 13.7 mean = 76.2 variance = 188.1 standard deviation = 13.7 mean = 80 variance = 199.5 standard deviation = 14.1 mean = 80 variance = 199.5 standard deviation = 14.1 mean = 76.2 variance = 188.1 standard deviation = 15.0 mean = 76.2 variance = 188.1 standard deviation = 15.0 mean = 87.5 variance = 73 standard deviation = 8.5
To find the mean, add up all the numbers in the data set and divide by the total number of numbers:
(55 + 87 + 62 + 85 + 93 + 75) / 6 = 457 / 6 = 76.2
To find the variance, first find the squared difference from the mean for each number, then find the average of those squared differences:
[(55-76.2)^2 + (87-76.2)^2 + (62-76.2)^2 + (85-76.2)^2 + (93-76.2)^2 + (75 - 76.2)^2] / 6 = (478.4 + 109.6 + 196.84 + 73.24 + 285.64 + 1.44) / 6 = 1145.16 / 6 = 190.86
To find the standard deviation, take the square root of the variance:
√190.86 ≈ 13.8
Therefore, the correct response is:
mean = 76.2
variance = 190.9
standard deviation = 13.8