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### Course: AP®︎/College Statistics > Unit 3

Lesson 5: More on standard deviation (optional)- Review and intuition why we divide by n-1 for the unbiased sample variance
- Why we divide by n - 1 in variance
- Simulation showing bias in sample variance
- Simulation providing evidence that (n-1) gives us unbiased estimate
- Unbiased estimate of population variance

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# Unbiased estimate of population variance

A CS program to help build intuition

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- The title of this page is, "Unbiased estimate of population variance", but doesn't this program measure the biased estimate?(44 votes)
- as the title says, it is about "estimating" the unbiased value using biased value. with sample sizes from 2 to 10, it shows a relation of (n-1)/n between the two, resulting in the division with the "n-1". for a sample size of 2 this is 1/2, and of 3 gives 2/3 and so on. it becomes "unbiased = biased *n/(n-1)" or simply the equation with "n-1" as the denominator.(5 votes)

- So what I'm getting is that the n-1 unbiased formula describes the phenomenon where the sample variance estimate is closer to population variance using n-1 than n. However, I don't understand why this phenomenon occurs? Why does using n to divide cause an underestimation in the first place?(12 votes)
- The underestimation arises from the fact that using n (the sample size) as the divisor doesn't fully account for the variability present in the sample (because n<N).(2 votes)

- In Population, N=463 but sample Size Vs variance has samples in thousands ?? How come it is possible?(2 votes)
- think about how many groups (=samples) of 2, 3, 4...or 10 you could build out of 463! Lets say it would be 463 people and you build groups of 2. How many different groups could you build? Combinatorics say 463C2, which is 463*462/2 which is 106,953 possibilities. But then you can also build groups of 3, of 4... and so on. There is a lot of possibilities to build samples!(15 votes)

- how do i find the variance of classified data?(2 votes)
- how do i find the variance of classified data?(4 votes)
- yeap this is biased one(3 votes)
- Can a population data be less than the sample data ?(3 votes)
- Yes, it's possible for population data to be less than sample data. This can occur due to random sampling variability or if the sample is not representative of the entire population. However, in ideal conditions, the sample data should provide a reasonable estimate of the population data.(1 vote)

- Are there any places to find practice questions on these lessons?(2 votes)
- guys this crazy :()(2 votes)
- In the Sample Statistics graph what happens to the sample variance as the sample mean increases?(1 vote)
- Without specific details about the Sample Statistics graph, it's challenging to provide a definitive answer. However, in general, as the sample mean increases, the sample variance may exhibit different behaviors depending on the distribution of the data. For example, in some cases, the sample variance may increase with the sample mean, while in others, it may decrease or remain relatively constant. Understanding these relationships can provide insights into the data's variability and distribution.(1 vote)