Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is 10 milligrams. Juan repeats the measurement 3 times and records the mean (x-bar) of his 3 measurements.
a) What is the standard deviation of Juan's mean result? (that is, if Juan kept on making 3 measurements and averaging them, what would be the standard deviation of all his means?)
==> I don't quite understand this concept...can someone please explain this to me? Thanks! :)
Standard deviation of a distribution of means = standard error of the mean = SEm
SEm = SD/√(n-1)
7.071?
Sure! I'd be happy to explain it to you.
In statistics, the standard deviation is a measure of the amount of variation or dispersion in a set of values. It tells us how spread out the values are from the mean (average). The standard deviation of Juan's lab measurements being 10 milligrams means that the measurements taken by all the students in the class have an average deviation of 10 milligrams from the mean measurement.
Now, to find the standard deviation of Juan's mean results, we need to consider the concept of sampling distribution. Sampling distribution refers to the distribution of all the possible sample means that can be obtained from a population of values. In this case, Juan is taking 3 measurements and calculating the mean of those measurements.
The standard deviation of a sampling distribution, often denoted by the symbol σx̄ (pronounced sigma x-bar), is determined by dividing the standard deviation of the population (σ) by the square root of the sample size (n). In this case, since Juan is taking 3 measurements, n=3.
So, to find the standard deviation of Juan's mean result, we can use the formula:
σx̄ = σ / √n
Plugging in the given values, we have:
σx̄ = 10 / √3
Therefore, the standard deviation of Juan's mean result is approximately 5.7735 milligrams.
I hope that clarifies the concept for you! Let me know if you have any further questions.