Find the standard deviation of the data set to the nearest tenth:
(21, 13, 18, 16, 13, 35, 12, 8, 15)
Answer: 16.8
thanks
The mean of the given numbers is 16.8.
SD=sqrt(1/N sum((x-mean)^2))
=sqrt(1/9*((21-16.8)^2+(13-16.8)^2...
=7.3
To find the standard deviation of a data set, you need to follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the mean of the squared differences.
4. Take the square root of the mean from step 3 to get the standard deviation.
Let's calculate the standard deviation for the given data set:
Step 1: Find the mean.
To find the mean, add up all the numbers in the data set and divide by the total number of values:
(21 + 13 + 18 + 16 + 13 + 35 + 12 + 8 + 15) / 9 = 151 / 9 = 16.78 (rounded to two decimal places).
Step 2: Subtract the mean from each data point and square the result:
(21 - 16.78)^2 = 18.58
(13 - 16.78)^2 = 13.99
(18 - 16.78)^2 = 1.49
(16 - 16.78)^2 = 0.61
(13 - 16.78)^2 = 13.99
(35 - 16.78)^2 = 339.85
(12 - 16.78)^2 = 22.92
(8 - 16.78)^2 = 75.48
(15 - 16.78)^2 = 3.16
Step 3: Find the mean of the squared differences.
Add up all the squared differences and divide by the total number of values:
(18.58 + 13.99 + 1.49 + 0.61 + 13.99 + 339.85 + 22.92 + 75.48 + 3.16) / 9 = 89.97 / 9 = 9.994 (rounded to three decimal places).
Step 4: Take the square root of the mean from step 3 to get the standard deviation:
√9.994 = 3.162 (rounded to three decimal places).
Therefore, the standard deviation of the given data set is approximately 3.162.