Find the variance for the given data. Round your answer to one more decimal place than the original data.
-The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below:
$21.1\quad14.8\quad39.1\quad37.6\quad17.4\quad24.2$
Compute the standard deviation s.
A)38.4
B)3962.9
C)4495.2
D)10.32

Question

Find the variance for the given data. Round your answer to one more decimal place than the original data.
-The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below: 
$21.1\quad14.8\quad39.1\quad37.6\quad17.4\quad24.2$ 
Compute the standard deviation s.
A)38.4
B)3962.9
C)4495.2
D)10.32

Quizplus · Accepted Answer

To find the variance, we first calculate the mean of the data, then use the variance formula which involves summing the squared differences between each data point and the mean, and finally dividing by the number of data points minus one (since this is a sample, not a population).1. Calculate the mean ($\mu$):$\mu = \frac{21.1 + 14.8 + 39.1 + 37.6 + 17.4 + 24.2}{6} = \frac{154.2}{6} = 25.7$2. Calculate the squared differences from the mean, sum them, and divide by $n-1$ (where $n$ is the number of data points, which is 6):Variance ($s^2$) = $\frac{(21.1-25.7)^2 + (14.8-25.7)^2 + (39.1-25.7)^2 + (37.6-25.7)^2 + (17.4-25.7)^2 + (24.2-25.7)^2}{6-1}$= $\frac{(-4.6)^2 + (-10.9)^2 + (13.4)^2 + (11.9)^2 + (-8.3)^2 + (-1.5)^2}{5}$= $\frac{21.16 + 118.81 + 179.56 + 141.61 + 68.89 + 2.25}{5}$= $\frac{532.28}{5}$= 106.456The standard deviation ($s$) is the square root of the variance. However, the question asks for the variance, not the standard deviation.Variance = 106.456 (rounded to one more decimal place than the original data, which is one decimal place, so we keep two decimal places)Since none of the provided options match the calculated variance directly and the question seems to have asked for the standard deviation but listed options that don't match our calculation, there seems to be a misunderstanding in the question's request versus the provided options. The correct calculation for variance has been provided, but the options seem to relate to a different calculation or a misunderstanding in the question's phrasing. The closest option related to standard deviation would be D) 10.32, which appears to be a mistake in the question asking for variance but providing options for standard deviation. The correct step was to calculate variance, which was done, but the final answer expected seems to be for standard deviation, which is the square root of 106.456, approximately 10.32.

Find the Variance for the Given Data 21.114.839.137.617.424.221.1\quad14.8\quad39.1\quad37.6\quad17.4\quad24.221.114.839.137.617.424.2 Compute the Standard Deviation S

Find the Variance for the Given Data $21.1\quad14.8\quad39.1\quad37.6\quad17.4\quad24.2$ Compute the Standard Deviation S