If the standard deviation of a sample is 4.3 for 28 data values, what would the standard deviation be fore the population from which the sample was drawn?
The standard deviation for a distribution of means is called the Standard Error of the mean (SEm).
SEm = SD/√n
To find the standard deviation for the population based on the sample, we can use the following formula:
Population Standard Deviation = Sample Standard Deviation / √(Sample Size)
Given:
Sample Standard Deviation (s) = 4.3
Sample Size (n) = 28
Let's substitute these values into the formula:
Population Standard Deviation = 4.3 / √(28)
Using a calculator, we can evaluate this:
Population Standard Deviation ≈ 0.810
Therefore, the standard deviation for the population from which the sample was drawn would be approximately 0.810.
To find the standard deviation for the population from which the sample was drawn, we can use the formula for the standard deviation of a sample:
σ = s / √n
Where:
- σ is the standard deviation of the population
- s is the standard deviation of the sample
- n is the number of data values in the sample
In this case, we have:
- s = 4.3 (standard deviation of the sample)
- n = 28 (number of data values in the sample)
Now we can plug these values into the formula:
σ = 4.3 / √28
To calculate √28, we need to find the square root of 28, which is approximately 5.2915.
σ = 4.3 / 5.2915
Now let's perform the division:
σ ≈ 0.8121
So, the standard deviation for the population from which the sample was drawn is approximately 0.8121.