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 = 87.5 variance = 73 standard deviation = 8.5 mean = 87.5 variance = 73 standard deviation = 8.5 mean = 76.2 variance = 188.1 standard deviation = 15.0 mean = 76.2 variance = 188.1 standard deviation = 15.0 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
To find the mean, add up all the numbers in the data set and divide by the total number of values:
(55 + 87 + 62 + 85 + 93 + 75) / 6 = 457 / 6 = 76.2
To find the variance, calculate the average of the squared differences from the mean:
((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 = (476.64 + 98.64 + 210.24 + 74.44 + 298.44 + 2.44) / 6 = 1160.84 / 6 = 193.4
To find the standard deviation, take the square root of the variance:
√193.4 = 13.9
Therefore, the correct answer is:
mean = 76.2, variance = 193.4, standard deviation = 13.9.