Measures of Variability
Measures of Variability
Measures of Variability
Measures of central tendency: typical or average value for a sample or population Can be misleading How are values distributed
Measures of variability
How much variability is there, in a sample, or in a population? Crude measure: Range = highest value minus lowest value More sophisticated measure of variability: Standard deviation
Standard deviation
Average of the differences between each individual score and mean of all scores? How far is average score from the mean? How scattered are the data?
Standard deviation:
ungrouped data
s=
(Y Y )
n
Standard deviation:
grouped data
s=
f (Y Y )
n
Y =
fY
= 1663/76 = 21.9
f
x0 x1 x6
fY
=0 =8 = 78
Y Y
(Y Y ) 2
f (Y Y ) 2
Standard deviation:
grouped data
s=
f (Y Y )
n
Standard deviation:
calculating formula
s=
fY
n
- ( fY / n)
Square of the means
Standard deviations:
calculating formula
Y 3 8 13 18 23 28 Y2 9 64 169 324 529 784 f 0 1 6 19 33 17 76 fY2 0 64 1014 6156 17,457 13,328 38,019 fY 0 8 78 342 759 476 1663
Standard deviation:
calculating formula
s=
Standard deviation
If the population is normally distributed, you can estimate the percentage of the population within 1, 2, and 3 standard deviations of the mean: 68% of cases lie +/- 1 s.d. of mean 95% of cases lie +/- 2 s.d.s of mean 99.9% of cases lie +/- 3 s.d.s of mean
Standard deviation
Y = 21.9