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5 votes
8, 10, 11, 12, 16, 20, 24, 28, 32, 33, 37

Using Statkey or other technology, find the following values for the above data. Click here to access StatKey.
The mean and the standard deviation. Round your answers to one decimal place.
mean = ____________ standard deviation = ________

1 Answer

3 votes

Answer:

Mean = 21.0

Standard deviation = 9.9

Explanation:

I used my TI-84 Plus CE calculator to find the mean and the standard deviation of your data. However, I will explain how to find the mean and standard deviation

First, I'll provide the steps to find the mean:

Mean:

Step 1: Find the sum of the data:

The sum of the data is given by:

8 + 10 + 11 + 12 + 16 + 20 + 24 + 28 + 32 + 33 + 37 = 231

Step 2: Divide this sum by the total number of data points:

There are 11 data points in your data set. Thus, we can find the mean by dividing 231 by 11:

Mean = 231 / 11

Mean = 21.0

Thus, the mean of the data is 21.0.

Now, I'll provide the steps to find the standard deviation:

Standard Deviation:

Step 1: Find the mean:

We've already determined that the mean of the data set is 21.0.

Step 2: Subtract the mean from each data point. Then, square the result:

(8 - 21.0)^2 = (-13)^2 = 169

(10 - 21.0)^2 = (-11)^2 = 121

(11 - 21.0)^2 = (-10)^2 = 100

(12 - 21.0)^2 = (-9)^2 = 81

(16 - 21.0)^2 = (-5)^2 = 25

(20 - 21.0)^2 = (-1)^2 = 1

(24 - 21.0)^2 = (3)^2 = 9

(28 - 21.0)^2 = (7)^2 = 49

(32 - 21.0)^2 = (11)^2 = 121

(33 - 21.0)^2 = (12)^2 = 144

(37 - 21.0)^2 = (16)^2 = 256

Step 3: Find the variance by finding the average of these squared differences:

Mean = (169 + 121 + 100 + 81 + 25 + 1 + 9 + 49 + 121 + 144 + 256) / 11

Mean = (1076) / 11

Mean = 97.81818182 (Let's not round at the intermediate step and round at the end).

Step 4: Take the square root of the variance to find the standard deviation:

Standard deviation = √(97.81818182)

Standard deviation = 9.890307468

Standard deviation = 9.9

Thus, the standard deviation of the data set is 9.9

User Wilberto
by
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