Problem

These data are the number of junk e-mails Lena received for 9 consecutive days.
$\begin{array}{lllllllll}61 & 1 & 1 & 4 & 2 & 30 & 22 & 5 & 9\end{array}$
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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.
Part 1 of 3
The range is 60 e-mails.
Part: $1 / 3$
Part 2 of 3
The variance is

Answer

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Answer

Final Answer: The range is \(\boxed{60}\) e-mails, the variance is \(\boxed{356.4}\), and the standard deviation is \(\boxed{18.88}\).

Steps

Step 1 :The given data represents the number of junk e-mails Lena received for 9 consecutive days: \(61, 1, 1, 4, 2, 30, 22, 5, 9\).

Step 2 :First, we need to find the range of the data. The range is the difference between the highest and the lowest number in the data set. In this case, the range is \(61 - 1 = 60\) e-mails.

Step 3 :Next, we need to find the variance. The variance is the average of the squared differences from the mean. To find the variance, we first need to calculate the mean of the data. The mean is the sum of all the numbers divided by the count of the numbers. The mean of the data is \(15\).

Step 4 :Then, we subtract the mean from each number in the data set and square the result. The variance is the average of these squared differences. The variance of the data is \(356.4\).

Step 5 :Finally, we need to calculate the standard deviation. The standard deviation is the square root of the variance. The standard deviation of the data is \(18.88\).

Step 6 :Final Answer: The range is \(\boxed{60}\) e-mails, the variance is \(\boxed{356.4}\), and the standard deviation is \(\boxed{18.88}\).

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