Video instructions and help with filling out and completing Where Form 2220 Compute

Instructions and Help about Where Form 2220 Compute

In this tutorial I'm going to talk about calculating the standard deviation in variance they're both related this isn't high definition so click on 720 before you click the fullscreen view the button right there a typical problem looks like this the following are the number of jobs a sample of six people applied for find the mean the variance and standard deviation blah blah blah what you really are interested in they're just the numbers and how to calculate the variance and standard deviation and that's what I'm gonna do here the sample standard deviation is equal to the square root of the sample variance and these are the symbols I'm going to use and the first thing I'm going to calculate is a sample variance the sample variance is this formula right here and we'll take the square root of that to get the standard deviation the X I that's the observations the x-bar that's the mean and we'll go through the calculations of these each one of these two and n is the sample size I'm going to make a little table to help me stay organized and recommend that you do the same I'm gonna put in the X which did my observation and then we'll put a little line horizontal line and I'm gonna do an up-and-down vertical line as well the next column is the mean x-bar that's the mean the sample mean put a little vertical line as well now I'll just put in all the observations and that's the same as above a line and I'm gonna put a couple more column headings in and you'll see I'll tell you what those mean as we fill them in but just go ahead and write them in now and that's the observation minus the mean squared so I need to calculate the mean and that's equal to the sum of all my observations divided by the number of observations so if I add up all my observations that call them right there that equals 84 now I take that 84 and I put it right on top of that equation right there and that's my numerator divided by 6 and ad equals the my mean which is 14 jobs now I take that 14 and put it right there in that column and when the whole column is gonna be filled with 4 teens now the next column over is the observation minus the mean like 17 minus 14 and of course that is equal to 3 then I have 15 minus 14 that's equal to 1 23 minus 14 that's equal to 9 7 minus 14 that's a negative 7 9 minus 14 that's negative 5 13 minus 14 that's negative 1 if I add up this column it should always add up to 0 always zero that's a good way to check your numbers 2 now my last column I take the previous column and I squirt so 3 squared is 9 1 squared is 1 9 squared is 81 negative 7 squared is 49 doesn't matter if we use a negative sign or not it's 49 same with 5 squared is 25 negative 1 squared is 1 I drop the negative sign but it's still always positive now I add up this column of information and it's 166 the 166 is actually the numerator of this of that equation so that's the same thing so I can say the sample variance which I have is s squared is equal to 166 divided by divided by n minus 1 n is 6 so it's 6 minus 1 which of course is 5 so the sample variance is equal to 33 point 2 now if I take that 33 point 2 and take the square root of that that's the sample standard deviation which is equal to s is equal to five point seven six now I'll summarize for you the sample variance is equal to thirty three point two jobs squared job squared is a unit sample standard deviation is equal to five point seven six jobs the sample mean is equal to fourteen jobs notice that the standard deviation and sample mean are in the same units which so they can be compared with each other as well and this has just been a slight review or introduction to calculus standard deviation and the variance