Question

a sample is analyzed five times by the same method to give the following results: 4.54, 4.89, 5.23, 5.12, 4.70. what is the standard deviation of the measurements?

Answer 1

The standard deviation of the measurements is 0.2859

Explanation:

n = number of terms = 5

We first find the mean, u

mean = sum of the values of terms / number of terms

`u = (4.54 + 4.89+5.23+5.12+4.70)/5`

u = 4.896

Finding standard deviation, S

`S = √((Sum(x-u)^2/(n-1))`

Finding the sum, we have,

`Sum(x-u)^2 = (4.54-4.896)^2 + (4.89 - 4.896)^2 + (5.23 - 4.896)^2+(5.12 - 4.896)^2+(4.70 - 4.896)^2\\Sum(x-u)^2 = 0.32692`

Now, then S will be,

`S = √((Sum(x-u)^2/(n-1))\\S = √(0.32692/(4))\\\\S = 0.2859`

Hence the standard deviation is 0.2859