Measures of Variability

Variability Def

a measure of how “close together” or “far apart” scores are in a data set

range def

the difference between the largest and smallest values in a data set

range formula

range = MAX-MIN

variance def

a measure of spread relative to the scatter of score values about their mean

Population variance formula

sample variance formula

Steps for calculating the same variance (5)

1. calculate the mean of the dataset

2. calculate the deviation of every score value from the mean

3. square all of the deviations

4. add all of the squared deviations

5. divide by n-1

Sample variance example

do iiiiittttt

standard deviation def

the square root of the variance

standard deviation example

you got it

first quartile formula

n +1/4

2nd quartile formula

2(n+1)/4

3rd quartile formula

3(n+1)/4

3 quartiles example

yep.. all three

box plot definition

a numerical summary of data consisting of the Min, max and all 3 quartiles

box plot example

do it

Innerquartile range def

the difference between the third and first quartile values

Innerquartile range formula

IQR = Q₃- Q₁

IQR example

yes ma’am you heard me

Advantage of the IQR

it is superior to the traditional range because it only looks at the variability of the middle 50% of the observations and is therefore less sensitive to extreme outliers

Outlier def

an observation whose value, X, either exceeds the value of the 3rd Quartile by a magnitude greater than 1.5IQR or is less than the value of the 1st quartile by a magnitude greater than 1.5IQR

Finding outlier example

yes, both high and low