Calculate the range population variance and population...

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 6,9,8,8,10,10,4,9,9,37

Transcript

00:01 Hello students we need to write here we need to calculate range population variance and population standard deviation we are given our data set so if i write here for this in the first case we need to write here range range is maximum value minus minimum value if i write here maximum value minus minimum value if i write here for this this must be 3xm minimum value minus minimum value 37 minus 4.

00:34 So if i write here for this, this must be 37 minus 4, which is we need to write here this is 33.

00:45 Now in the second case, what we need? we need our population variance.

00:50 So this must be, so to calculate this first we need to calculate our x bar, which is our mean value which is basically if i write here sum of data divided by number of data so this will be calculated as if i write here for this this is 6 and 15 15 plus 60 is 31 31 31 plus 10 40 15 this is 55 55 plus 18 if i write here for this this must be 55 plus 18 plus 37 plus 18 plus 37 which would be 110 this must be divided by if i write here for this total values are so basically one two three four five six seven eight nine ten which is ten so this is eleven now what we need right here for calculating our variance we need to write here so we are calculating our population variance not single variance this is population variance sigma square this must be sigma square which can be written as submission of x i minus mu so this is basically equivalent to mu to so we need to consider here x -par let's say so we are considering x -par to make it more clear raise to power two divided by if i write here for this this must be n so finally what we gain right here this is we are going to write so let's start this this is x i it means that six minus 6 minus 11 raised to power 2 plus if i write for this 9 minus 11 raised to power 2 dot dot dot so if i write here this must be 37 minus 11 raised to power 2 37 minus 11 minus 11 raise to power 2 and if i write here for this this will be this will be calculated as divided by 10 so if i write here for this, this total value would be 782 divided by 10, which is 78 .2.

03:43 And now we need our population standard deviation.

03:48 So we need to write here this is population standard.

03:55 Population standard deviation is under root of 78 .2...

Question

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 6,9,8,8,10,10,4,9,9,37

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