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