SAS 12 MEASURES OF VARIABILITY

dispersion and variability

• generally that mean same thing in statistics

• they both refer to how spread out or scattered the data values are in a dataset

outlier

• is a data point that is significantly higher or lower than most of the other values in a dataset

• can affect variability measures like the range and standard deviation 

consistency

• refers to how similar or close the values in a dataset are to each other 

• less variability means higher consistency

skewed distribution 

• is where data is not evenly spread, and one tail is longer than the other

symmetric distribution

• is where the left and right sides are mirror images of each other

• the mean and median are usually the same or very close

positively skewed

• right skewed

• tail is longer on the right

• mean is greater than median

negatively skewed 

• left skewed 

• tail is longer on the left

• mean is less than the median 

measures of variability

• also called “measures of dispersion”

• are statistical tools used to describe how spread out or scattered the values in a dataset are

• helps us understand our numbers better

range 

• looking at the biggest and smallest numbers to see how far apart they are

variance and standard deviation

• show how spread out or close together numbers are in a dataset

• close numbers=small difference

• scattered numbers=big difference

• helps us see if our numbers are close together or spread out, which is important to know

variance

• shows how much the data points differ from the mean

• imagine you are trying to figure out how much the scores of students in a class vary from the average score

sample variance 

• is like measuring how spread out those scores are from the average 

• helps us understand id the scores are close together or spread out widely 

standard deviation

• provides an average measure of how far the data points are from the mean and is derived from the variance

sample standard deviation

• is like a tool we use to see how spread out the numbers are in a small group compared to the average number in that group

• helpful since it gives us a sense of how much the entire group might vary

interquartile range IQR 

• Is the range of the middle 50% of a data set, calculated as Q3 − Q1, where Q1 is the first quartile and Q3 is the third quartile.