Karl Pearson’s Idea - Standard Deviation

[Pages:3]Karl Pearson's Idea - Standard Deviation

Karl Pearson (1857 ? 1936)

If you have a group of numbers the mean average: ? is an accepted way to get a single number to represent the group ? it doesn't tell you how spread out the numbers in the group are ? stuff like that can be important

Pearson wanted to come up with a second calculation you could use along with the mean average that would tell you how spread out the numbers in the group were.

Pearson came up with this: ? work out the mean average for the group ? work out the individual difference between each number and the mean average ? he thought of these differences as "deviations" from the mean ? he combined the mean and the differences into a formula ? he called it standard deviation ? we think he used the word "standard" because he wanted it to become the standard way statisticians would measure how spread out the data was in a group

Karl Pearson's standard deviation formula (1894)

(xi - mean)2

standard deviation = n

Here it is explained in words:

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6

Work out the mean of your set of numbers Work out the difference between each number and the mean Square each difference Add up the squares of all the differences Divide by the number of values in your set (this is called the variance) Take the square root of the variance to get the standard deviation

These take absolutely ages to do by hand ? see next page.

I'll get you to do one example in class by hand with a calculator. No one does them that way in real life, they use computer software. We'll use the function in EXCEL in the assessment.

Standard Deviation Calculation for Team A

Team A 40 mins 55 mins 58 mins 63 mins

Step 1

Work out the mean average 40 + 55 + 58 + 63 = 216 216 ? 4 = 54

Step 2

Work out the difference between each number and the mean

40 - 54

55 - 54

58 - 54

63 ? 54

= -14

= 1

= 4

= 9

Step 3

Square the differences

-142

-12

= 196

= 1

42 = 16

92 = 81

Step 4

Add up the squares 196 + 1 + 16 + 81 = 294

Step 5

Divide by the number of values in the group (variance) 294 ? 4 = 73.5

Step 6

Take the square root to get the standard deviation

73.5 = 8.5732141

rounded to one decimal place it's 8.6

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