Module 7--Measures of Variability Flashcards
What do the measures of Variability Provide?
The measures of variability provide information about how the values within a distribution vary.
What are the Measures of Variability?
■ Information about dispersion or spread – A measure of variability provides information regarding the amount of dispersion or spread, that exists within a set of data.
■ Relative perspective – If we know a distribution’s variability, we can put individual observations into relative perspective.
■ Are observations different from the mean? – Measures of variability serve as tools for understanding not just whether observations are different from some designated location, such as the mean, but how much they vary. In other words, they provide a benchmark for determining how unusual a value is.
What are the THREE KEY MEASURES of VARIABILITY
■ Range – (1) for a set of data, the difference between the maximum value and the minimum value; (2) for a pay grade, the percentage by which the maximum pay exceeds the minimum.
■ Interquartile range – the difference between the 25th percentile (first quartile) and the 75th percentile (third quartile) in an ordered array of data. This range contains the middle 50 percent of the data.
■ Standard deviation – the square root of the average squared difference between data points and the mean. Standard deviation is a measure of variability which indicates an average relative distance between each data point and the mean. The larger the standard deviation, the more
What is RANGE
Range = Highest Value - Lowest Value
Easiest to understand – The range is our easiest measure of variability to understand.
■ Easily calculated – The range is easily calculated.
■ At least ordinal level data – The range is appropriate for data that satisfy at least the ordinal level
of measurement.
■ Distance between highest and lowest points – The range is a measure of variability that tells us
the distance between the highest and lowest data points in our distribution.
What is Interquartile Range?
The interquartile range is a measure of variability
based on the distance between the 75th and 25th
percentiles for our distribution.
Interquartile Range = P75 - P25
= Q3 - Q1
Remember for INTERQUARTILE RANGE….
■ The range is based on two values – The range is based on only two values. It does not reflect the
variation of the values between these two points.
■ Interquartile range based on middle 50% of data – The interquartile range is based on only the
middle 50% of the data. It does not reflect the variation of the full set of data either.
■ Is there a better measure? – We need a better measure - …one that is based on all of the values in
our data set.
* The measure we need to do this is called the standard deviation.
What is STANDARD DEVIATION?
A measure of variability that indicates an average relative
distance between each data point and the mean
■ Uses all data points – The standard deviation uses all the data points from the data set in its
calculation.
■ Most useful measure – The standard deviation is the most useful measure of variability in statistics.
■ Definition – The standard deviation is the “square root of the average of the squared deviations from the mean.”
* If the standard deviation is relatively small, the data points tend to be relatively close to the mean.
* If the standard deviation is relatively large, the data points tend to be relatively far away from the mean.
What are some application of the STANDARD DEVIATION (pAGE 195)
- Identify outliers
- Compare variation in data sets
- Create confidence intervals
- Compute z-scores
N = number of data points
X = the data values
X = the mean of all n data
points (x-bar)
Measures of Variability: Standard Deviation
Ʃ = sum of
= standard deviation of the population
sx = standard deviation of the sample
