Find the mean and standard deviation of the data set. If necessary, round to the nearest hundredth.
4, 8, 5, 12, 3, 9, 5, 2
Mean is 6 and standard deviation is about 13.33?
That standard deviation is much too big. Are you sure it is not the variance and you forgot to take the square root?
mean is 6 yes
I get sqrt 80 = 8.94 for SD
2^2 + 2^2+1^2+6^2+3^2+3^2+1^2+4^2
4+4+1+36+9+9+1+16 = 80
sqrt 80 = 8.94
Damon, I think you forgot to divide by 7 before taking the square root.
SD = √(80/7) = 3.3806
The amazing Wolfram supports this
http://www.wolframalpha.com/input/?i=standard+deviation+4%2C+8%2C+5%2C+12%2C+3%2C+9%2C+5%2C+2
whoops, sorry, thanks !
To find the mean and standard deviation of a data set, follow these steps:
1. Calculate the mean:
- Add up all the numbers in the data set: 4 + 8 + 5 + 12 + 3 + 9 + 5 + 2 = 48
- Divide the sum by the total number of values in the data set: 48 ÷ 8 = 6
So, the mean of the data set is 6.
2. Calculate the sum of squares:
- Subtract the mean from each number in the data set, square the result, and sum these squares:
(4-6)^2 + (8-6)^2 + (5-6)^2 + (12-6)^2 + (3-6)^2 + (9-6)^2 + (5-6)^2 + (2-6)^2
(-2)^2 + (2)^2 + (-1)^2 + (6)^2 + (-3)^2 + (3)^2 + (-1)^2 + (-4)^2
4 + 4 + 1 + 36 + 9 + 9 + 1 + 16 = 80
3. Calculate the variance:
- Divide the sum of squares by the total number of values in the data set: 80 ÷ 8 = 10
So, the variance of the data set is 10.
4. Calculate the standard deviation:
- Take the square root of the variance: √10 ≈ 3.16
So, the standard deviation of the data set is approximately 3.16.
Therefore, the mean is 6 and the standard deviation is about 3.16.