standard deviation

Question

whats the standard deviation of the data set below, Rounding your answer to three decimal places?

2, 4, 6, 6, 8, 10, 11, 12, 14, 16, 17, 18, 18, 18

Answer 1

Finding the standard deviation begins with finding the mean or average.

 

Here the mean, µ = (2+4+6+6+8+10+11+12+14+16+17+18+18+18)/14 = 80/7.

 

Next, we find the Sum of the Squared Deviations, or SSD.

 

The deviations are found by subtracting the mean, µ = 80/7, from each of the data.

 

So 2-80/7 = -66/7 is the first. 

4- 80/7 = -52/7.

6-80/7 = -38/7.... and so on for the rest of the data points.

 

Adding up the squares of these deviations gives us the SSD, or Sum of Squared Deviations.

 

So SSD = (-66/7)^2 + (-52/7)^2 + (-38/7)^2 + ... + (46/7)^2 = 2838/7.

 

The variance, σ² = SSD/n, where n = 14 is the number of data points.

 

So here σ² = SSD/n = (2838/7)/14 = 1419/49.

 

The standard deviation, σ = √(σ²) = 5.381.

 

If we were considering these data a sample, and looking for the sample standard deviation instead, we would use the sample variance s² = SSD/(n-1), or s² = (2838/7)/13 = 2838/91. Note the (n-1) where σ² used n.

 

This gives a sample standard deviation of s = √(s²) = 5.585.

 

I hope this helps and if you'd like me to explain any steps further please ask. I'll be glad to help.