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### Course: Statistics and probability>Unit 13

Lesson 2: Comparing two means

# Difference of sample means distribution

Sal walks through the difference of sample means distribution. Created by Sal Khan.

## Want to join the conversation?

• At "We saw this in the last video".
where is the last video?
I can't find the lecture content in last videos.
So I don't understand lecture content at .
Plese help me. . .
• I think it's this video: Variance of differences of random variables under the Random Variables section of Statistics and Probability
• A general statistical question - so much of the emphasis is placed on the mean as being representative of a given population, but what is the use of the population mean, and indeed the sampling distribution of the sample mean, when our population is not normally distributed?
• The population mean of X will be equal to the mean of the sampling distribution of X whether the population is normally distributed or not.
When our sample size of the population is high and if we gather a lot of the samples, we can plot the means of each sample on a graph and the mean of all of these means will still be the population mean. This is called the central limit theorem
Sal uses an app as a great visual demonstration of this here
• I am struggling to differentiate between when the variance of a sample is sigma squared divided by n and when it is sigma squared divided by (n+1). I know that sigma squared divided by (n+1) is a better estimator, and is actually unbiased, but why would Sal be using sigma divided by just "n" in this video? Am I missing a crucial point?
• The variance of a set of numbers is the Σ(x - x̄)²/n. You use this when you know every number in the set. If you take a sample, then this is how you calculate the variance of that sample.

However, if you want to estimate the variance of the population based on a sample, then it is Σ(x - x̄)²/ (n-1) for every x in the sample. This is because you don't know every x in the whole population. In this video Sal is talking in abstract terms, so assuming you know every value in a sample.

• Thanks for the fab videos,
I notice that they have been reorder since being recorded. In this one Sal often refers to "in the last video", but he is not referring to the one before in this sequence of videos. It would be great if you had a pointer to the video Sal is referring to.
kind regards and many thanks
Barry
• Saying Z = x^ - y^ after many videos using the Z distribution was very confusing lol
• Is there a video somewhere about paired differences? I would love to see those worked out!
Thank you for your videos, I love them!
• i have a question about a question i am doing for homework. dont have to answer the question its self, if someone could kind of clarify. "samples are taken from a normal population, will the distribution of the sample means also be normal?" what does it mean "distribution of the sample means"? i realize this is probably obvious but...
• for someone having a hard time with digesting what on earth "a distribution of sample" means, here's a bit weird derivation

1. get a population distribution
1) say you have 13 cats
2) they have 13 weights
3) you plot them on a graph
> this is a population distribution (of their weights)

2. get a sample (not sampling distribution!)
1) you pick 3 cats among 13 at random
2) plot their weights
3) you got 1 sample distribution of n=3 of your cats from the population distribution above

3. get a sampling distribution
1) you do 2 above ten times with the same n=3
2) plot their means on a graph (only 10 means of 3 cats, not any real weights of each cats!)
3) now you get your sampling distribution

when we are talking about "distribution of the sample means", we mean the 3-3) than 2-3). it literally means how distributed the 10 means of your 10 samples with 3 sample size for each from a population of 13 cats are!

hope this to sweep away the fog in your head (as it did for mine)
• If the means of X and Y are sufficiently far enough apart could the distribution diagram have two vertices?