Why are degrees of freedom (n-1) used in Variance and Standard Deviation 

Still looking forward to the video on degrees of freedom

+d00niepwns Because n-1 gives you a better estimate of the true population mean. Also because you are attempting to estimate a specific, usually unknown number. If you know the population mean you don't need to use n-1, you can just use n, as you aren't estimating anything.

why is (n-1) istead of other adjustment,such as (n-2)? why wen choose degree freedom as numerator?

d00niepwn

I thought this was clearly explained within 1 and a half minutes....

I agree the video is 100% misleading.

I agree. I don't see any reason why (n-1) is prefered. The difference decreases between n & (n-1) along with the increase of sample, and a data will always has big enough sample

agreed

John Paul Thanks John Paul! If you get a chance make sure you like and share the videos, it will make it easy for others to find them.

never mind, i still think this is a good explanation, though not directly. But with a little bit of sense of self taught , one should be able to figure out the reasons by themselves. The blames are just too mean.

Thanks

Imagine you start with two points. Pick any one point assuming it's fixed, then the only variation depends on how the left one varies from it. When we have three points, with any one point fixed, there are two variations because the left two points are free to move. That's the idea of degree of freedom. With any value of the sample fixed, the left n-1 values have the freedom to move within the interval so there are n-1 degrees of freedom.

+Shijie Wang Thanks for the explanation. But where does the idea of "fixed" points come into play? In a data set, what is assumed to be a fixed point? And why is there only one?

@@sjwang3892 excellent point. agger.

I agree. It sounds quite arbitrary to me too. If I had to guess, I'd say -1 allows you to make the adjustment but not by a wild lot. It's a very cautious adjustment, and also a safe thing to do mathematically (you won't get 0 or negative, assuming your sample size is >1), therefore -1 becomes the convention? My feeling is n-1 isn't chosen because it's DOF - it just happen to also be DOF... I'm no mathematician so anybody who has the answer please correct me.

I think it's Keynote.

Lorie Lorraine Interpreter You are welcome and happy my videos saved you from your tests. If you get a chance like MyBookSucks FB page at www.Facebook.Com/PartyMoreStudyLess , this will help others find the videos.

You are an amazing educator. I have been tasked with reviewing some other teaching materials as well as assisting with streamlining or improving our on-line classes here at a local community college - in Hawaii. If I could only replicate your level of engagement I'm certain I could increase the effectiveness of our programs. I'm so honored that you responded as I admire your work and would abandoned all of my career aspirations and "fetch" for you - just to have the chance to learn how to synthesize information the way you do. Might I add that the high quality of your video, the speed of your voice and intonation creates a top notch work product, the likes of which are NEVER seen on youtube - or anywhere else for that matter. Please keep up the great work as you inspire me. My entire study group now tunes in. Would you consider serving as my virtual mentor in the hopes of helping me better serve our Deaf and Visual learners and community. Mahalo & Aloha!

+Keng King Well, I am glad my videos are helping you. If you get a chance, like and share some of the videos. Also like my facebook page (www.FaceBook.Com/PartyMoreStudyLess). This will help others find the videos.

+Diana Adamczyk You are very welcome. I try to take complex ideas and simplify them. If you get a chance, then like, share the videos. This will help others find the videos too. (www.FaceBook.Com/partymorestudyless)

Somilas GH You are very welcome!!! Hopefully you will like, share, subscribe, If you get a chance could you please like our FB page. www.FaceBook.Com/PartyMoreStudyLess It will help others find the videos.

Veenit Shah I use a lot of different types of software from Adobe Flash, Illustrator, Garage Band and Final Cut Studio. Unfortunately there is not one single tool and I string them to together using a variety of different software products. Each minute of video takes me about 8 house of work.

statisticsfun well i would like to thank you for your time. Really appreciated your work

where are you working now?

+Erin Bartos For a sample, yes. If you have data for the whole population your degrees of freedom = N (as you aren't estimating an unknown number)

+Sami H Thanks for that. If you get a chance share and like the videos. Also like MyBookSucks FB www.FaceBook.Com/PartyMoreStudyLess.

+mirus Why n-1?Why divide by n-1 rather than N in the third step above? In step 1, you compute the difference between each value and the mean of those values. You don't know the true mean of the population; all you know is the mean of your sample. Except for the rare cases where the sample mean happens to equal the population mean, the data will be closer to the sample mean than it will be to the true population mean. So the value you compute in step 2 will probably be a bit smaller (and can't be larger) than what it would be if you used the true population mean in step 1. To make up for this, we divide by n-1 rather than n.But why n-1? If you knew the sample mean, and all but one of the values, you could calculate what that last value must be. Statisticians say there are n-1 degrees of freedom

latesq1 Same reason as for standard deviation. It is just an adjustment made when sample sizes are small. As sample sizes become larger the degrees of freedom do not make any difference.