variability key concepts

range:

• difference between the highest and lowest score in sample or population

• quick but crude way to describe the spread of a distribution

• can be misleading at times:

  • based on only the highest and lowest scores, so if there is an outlier the range will not be representative of the data

  • does not capture variability within a given range

variance:

average of the squared variations

Population variance formula:

σ²=Σ (X-μ)²/N

sample variance formula:

s²= Σ (X-M)²/N-1

μ or M represent the

mean

sum of squared deviations=

Σ (X-M)²)

what does squaring deviations do to distant scores

puts additional emphasis on them

standard deviation is another commonly used measure of

variability

population standard deviation formula:

σ=square root[Σ (X-mu)²/N]

sample standard deviation formula:

s= square root[Σ (X-M)²/N-1]

standard deviation is the _____ of the variance. the advantage of the SD is it _____ the squaring and puts the measure of variability in the same units as the sample score

• square root

• reverses