I got 45 for the range but I can't figure out the variance or standard deviation. Please help and show work so I can understand how to do this. Thanks.
+128474 Find the average = [ 35 + 50 + 60 + 60 + 75 + 65 + 80 ] / 7 = 425 / 7
Take each value and subtract it from the average, then......square these differences
So we have
diff square
425/7 - 35 = 180/7 ⇒ 32400/49
425/7 - 50 = 75/7 ⇒ 5625/49
425/7 - 60 = 5/7 ⇒ 25/49
425/7 - 60 = 5/7 ⇒ 25/49
425/7 - 75 = - (100/7) ⇒ 10000/49
425/7 - 65 = -(30/7) ⇒ 900/49
425/7 - 80 = - (135/7) ⇒ 18225/49
Take the average of the last column =
[ 32400 + 5625 + 25 + 25 + 10000 + 900 + 18225) / 49 / 7 = 9600 / 49 this is the variance
The square root of this is the standard deviation = √[9600/49] ≈ 14
