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Describing Data – Measures of Variability and Spread
Goals:
•
Learn how to describe the spread (or variability) of a data set
•
Calculate the range, inter-quartile range, variance, and standard deviation
•
Use technology to make calculations easier
CLASS NOTES
Questions/Main Ideas
Name _________________________________
Date _____________
Measure of spread:
The range
A statistics class, on the first day, took a poll as to what each student thought
their final grade in the course would be. The following data was collected:
76 81 100 100 92 96 80 83 95 100 93 93 82 93 100 70 80 93
Measures of position:
Quartiles
Interquartile range (IQR) –
the “width of the middle
50%”
Spread about the median...
Variance
Consider the following small data set: 3, 7, 10, 12
A typical squared deviation
about the mean
Standard Deviation
A typical deviation about
the mean
Do I really have to do this
by hand?
R
data <- c(76,81,100,100,92,96,80,83,95,100,93,93,82,93,100,70,80,93)
mean(data)
median(data)
var(data)
sd(data)
Graphing calculator
Stat → Edit (Enter the data)
Stat → Calc → 1VarStats
library(s20x)
data <- c(76,81,100,100,92,96,80,83,95,100,93,93,82,93,100,70,80,93)
options(digits=4)
summaryStats(data)
data <- c(76,81,100,100,92,96,80,83,95,100,93,93,82,93,100,70,80,93)
options(digits=3)
quantile(data,type=2)
Resistant?
Consider the following two data sets:
Set 1: 1,3,3,5,6,6,9,10
Range
IQR
Variance
Standard deviation
Set 2: 1,3,3,5,6,6,9,10,250