Answer:
13.6
Explanation:
To find the standard deviation of a sample of data, we need to follow a few steps:
Calculate the mean of the data set by adding up all the values and dividing by the number of values.
Subtract the mean from each individual data point to get the deviations from the mean.
Square each deviation to get the squared deviations.
Add up all the squared deviations.
Divide the sum of the squared deviations by the sample size minus 1 to get the sample variance.
Take the square root of the sample variance to get the standard deviation.
Let's apply these steps to the given data set:
The mean of the data set is (45+46+47+60+62+61+73+56+59+71+72+59)/12 = 59.5.
The deviations from the mean for each data point are:
45 - 59.5 = -14.5
46 - 59.5 = -13.5
47 - 59.5 = -12.5
60 - 59.5 = 0.5
62 - 59.5 = 2.5
61 - 59.5 = 1.5
73 - 59.5 = 13.5
56 - 59.5 = -3.5
59 - 59.5 = -0.5
71 - 59.5 = 11.5
72 - 59.5 = 12.5
59 - 59.5 = -0.5
The squared deviations for each data point are:
(-14.5)^2 = 210.25
(-13.5)^2 = 182.25
(-12.5)^2 = 156.25
(0.5)^2 = 0.25
(2.5)^2 = 6.25
(1.5)^2 = 2.25
(13.5)^2 = 182.25
(-3.5)^2 = 12.25
(-0.5)^2 = 0.25
(11.5)^2 = 132.25
(12.5)^2 = 156.25
(-0.5)^2 = 0.25
The sum of the squared deviations is 1079.
The sample variance is the sum of the squared deviations divided by the sample size minus 1, or (1079/(12-1)) = 183.7.
Finally, the standard deviation is the square root of the sample variance, or sqrt(183.7) = 13.6 (rounded to one decimal place).
Therefore, the standard deviation of the given data set is 13.6 minutes.