Chapter 4-Variability: Lecture Flashcards
variability
- refers to how much scores in a dataset differ from each other
- how the scores are scattered around the central point
- the concept of spread in the data
Why measure variability?
- It describes the data set’s distribution (clustered vs. spread out)
How can variability be measured?
- with the range
- with the variance/standard deviation
in both cases, variability measures distance
Range v1
highest score - lowest score
dataset: 3,7,8,9 range= 6
Range v2
lowest score and highest score (ex. 3 to 9)
range limitations
- range is useful as a very rough approximation of variability (ex. scores on an exam)
- But, it is an imprecise and unreliable measure of variability, as it is based on two scores (not all)
When using the man what do we compute to describe variability in the data?
- the variance and standard deviation
Variance definition
the average squared deviation from the mean
-raw way to measure variability
Standard deviation
- the most common measure of variability
- measures the average distance from the mean for scores in a dataset
- variance determines standard deviation
- useful way to measure variability
Sum of squares
the sum of the squared deviations
variance
the average of the squared deviations
standard deviation
the square root of the variance
Standard deviation self- check
- the SD can never be less than the distance between the mean and the least deviant score
- the SD can never be greater than the distance between the mean and the most deviant score
notes about n-1
- for samples we divide by the n-1 when calculating the variabce to inflate the variance estimate
- n-1 is the degrees of freedom (df) for S
- accounts for the fact that sample variance will typically underestmate population variance
- the effect is stronger with smaller samples and the effect of df helps account for that too
What happens if a constant is added or subtracted to every score?
- the standard deviation will not be changed
- the spread/variability does not change
What happens if a constant is divided or multipled to every score?
- the SD will be multiplied or divided by the same constant
- it will multiply the distance between scores, and the sd measures this distance
mean and SD as descriptive statistics
- mean and sd do a good job of describing most distributions, particulary if there isnt too much skew
- if given mean and standard deviation you can construct a rough sketch of the distribution