Problem

Ten used trail bikes are randomly selected from a bike shop, and the odometer reading of each (in miles) is recorded as follows.
$\begin{array}{llllllllll}1908 & 109 & 659 & 1901 & 784 & 359 & 216 & 369 & 227 & 658\end{array}$
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Find the range, variance, and standard deviation. Round the variance to one decimal place and the standard deviation to two decimal places, if necessary.
The range is

Answer

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Answer

Final Answer: The range is \(\boxed{1799}\), the variance is \(\boxed{394166.4}\), and the standard deviation is \(\boxed{627.83}\).

Steps

Step 1 :First, we arrange the data in ascending order: 109, 216, 227, 359, 369, 658, 659, 784, 1901, 1908.

Step 2 :The range of a set of data is the difference between the highest and lowest values in the set. To find the range, we subtract the smallest value from the largest value. So, the range is 1908 - 109 = 1799.

Step 3 :The variance is a measure of how much values in the set deviate from the mean. To find the variance, we first calculate the mean of the data, then subtract the mean from each data point, square the result, and finally take the average of these squared differences. The variance is 394166.4.

Step 4 :The standard deviation is the square root of the variance. It is a measure of the amount of variation or dispersion of a set of values. The standard deviation is approximately 627.83.

Step 5 :Final Answer: The range is \(\boxed{1799}\), the variance is \(\boxed{394166.4}\), and the standard deviation is \(\boxed{627.83}\).

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