Use the five numbers $18,17,13,14$, and 13 p to complete parts a) through e) below.
a) Compute the mean and standard deviation of the given set of data.
The mean is $\bar{x}=15$ and the standard deviation is $s=2.35$.
(Round to two decimal places as needed.)
b) Add 20 to each of the numbers in the original set of data and compute the mean and the standard deviation of this new set of data.
The new mean is $\bar{x}=35$ and the new standard deviation is $s=2.35$.
(Round to two decimal places as needed.)
c) Subtract 10 from each of the numbers in the original set of data and compute the mean and the standard deviation of this new set of data.
The new mean is $\bar{x}=\square$ and the new standard deviation is $s=\square$.
(Round to two decimal places as needed.)
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Answer
\(\boxed{\text{The new mean is } \bar{x}=5 \text{ and the new standard deviation is } s=2.10}\)
Step 1 ：Given the original set of data [18, 17, 13, 14, 13].
Step 2 ：Subtract 10 from each number in the original set of data to get the new set of data [8, 7, 3, 4, 3].
Step 3 ：Calculate the mean of the new set of data by adding up all the numbers and dividing by the number of numbers. The new mean is \(\bar{x}=5\).
Step 4 ：Calculate the standard deviation of the new set of data. First, find the variance, which is the average of the squared differences from the mean. Then take the square root of the variance to get the standard deviation. The new standard deviation is \(s=2.10\).
Step 5 ：\(\boxed{\text{The new mean is } \bar{x}=5 \text{ and the new standard deviation is } s=2.10}\)
