advertisement

Standard Deviation Problem Here are the scores: 55 67 65 54 55 51 58 57 61 49 __ Although we wouldn't have to, it might make it easier to arrange them from high to low or low to high. ----------------------------- There! This makes it easier to spot the mode, find the median, calculate the range, and get a feel for the mean. We'll need the mean in a moment in order to do the variance and standard deviation, so let's find it first. The sum of the Xs is 572. The N is 10. So the mean is 57.2. 49 51 54 55 55 57 58 61 65 67 ___ Let's make a table that looks like this one. It's a good idea to set this up this way any time we are expecting to do descriptive statistics. Scores 49 51 54 55 55 57 58 61 65 67 - the mean 57.2 57.2 57.2 57.2 57.2 57.2 57.2 57.2 57.2 57.2 =____ -8.2 -6.2 -3.2 -2.2 -2.2 - .2 .8 3.8 7.8 9.8 ____ 00.0 Square it! 67.24 38.44 10.24 4.84 4.84 .04 .64 14.44 60.84 96.04 ______ 297.60 2 _ 2 Now for the formula: s = (X - X) _________ N 2 Let's plug in the numbers: s = (297.60) ________ = 29.76 10 2 2 s is the variance. To get rid of the , take the square root of 29.76, 5.46. The standard deviation is 5.46.