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# Inferring population mean from sample mean

Much of statistics is based upon using data from a random sample that is representative of the population at large. From that sample mean, we can infer things about the greater population mean. We'll explain. Created by Sal Khan.

## Want to join the conversation?

• Did he draw those guys? They are good
• But how could you estimate the percent of the whole population using the sample?
• When using a sample to estimate a measure of a population, statisticians do so with a certain level of confidence and with a possible margin of error. For example, if the mean of our sample is 20, we can say the true mean of the population is 20 plus-or-minus 2 with 95% confidence. In other words, we are 95% sure that the true mean of the population is between 18 and 22.
• What is the difference between sample and population mean?
• population mean is the arithmetic mean of the whole population. For large groups (say all adult males in the united states), finding this mean is impractical. But we are not lost. We can use sampling to estimate the population mean (which we cannot know for certain). Suppose we want to know the mean height of adult males in the U.S. We could randomly select a sample of 50 men and calculate their average height. This would give us our sample mean.

This distinction is important and it is the reason that we need inferential statistics. We cannot measure what we want to know (population mean), but we can use statistical techniques to estimate the population mean to some desired degree of accuracy with a desired likelihood of being correct. The Central limit theorem tells us that the distribution of the sample means that we get any time we sample are normally distributed around the mean of the our population (the thing we want to know but cannot calculate directly). So if we choose our sample size large enough and ensure that our sample is randomly selected we can state the the sample mean that we calculate is within some range of the actual population mean (based on our sample standard deviation) with a certain degree of certainty (usually 95% or 99.7%).
• At what do you mean by geometric and arethmatic mean because I'm confused?
• Geometric and arithmetic mean have different meanings in some areas of math. For now just use the mean you've learned so far.
• the mean of 16 numbers is 8.if z is added whats is the new mean
• If the mean of 16 number is 8, that means you have 16 values (a, b, c, ... , p) whose average is 8.

(a + b + c + ... + p)/16 = 8. So, in other words: a + b + ... + p = 8 * 16 = 128

If you throw in a new number "z" into the mix, then you would have:

(a + b + ... + p + z) / 17 = (128 + z) / 17

This is approximately, 7.5294 + 0.588z as the new mean.
• What does that weird looking E mean?
• It's the greek letter 'Sigma'. It just means that you add up everything in a list. It's just a symbol for people who read maths so they know what is going on in the equation.
• At , I don't see the difference. They look practically identical.
• At , what is the funny looking E thing?
• What does the dash over x stand for?
Thank You
• it states that x-bar (x̄) is the sample mean.
that is the sum of all the entries in your sample divided by the amount of entries
or {x+x1+x2+...+xn}/n

for example:
You have 9 bags of lollies and you want to find mean amount of lollies.

1 bag has 6 lollies, another has 7 ,another 3, 5, 8,4,10 8, and the final bag has 12.
so the the sample mean or x-bar (x̄) would be:
x̄=(6+7+3+5+8+4+10+8+12)/9

so the mean or x-bar is x̄=7