# STAT 2000 Lecture Notes - Lecture 4: Interquartile Range, Box Plot

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January 20, 2017
2.3 Measuring Quantitative Data Continued
Symmetric Data: mean=median
Right Skewed: mean>median
Left Skewed: mean<median
If data is skewed, the median is preferred
Variability
o Wider range of #s=most variability
o Range: difference between smallest and largest observations
2.5 Using Measures of Position to Describe Variability
The P’th percentile is a value such that p percent of observations fell below or at that
value
Useful percentiles=quartiles
o Q1= 25th percent
o Q2= 50th percent
o Q3= 75th percent
EX. 13 Manual Dexterity
o Median=9.25 (9.1+9.4=18.5/2=9.25)
o Q1=median of the first half of the data: 7.1-9.1
8.3+8.3=16.6/2=8.3
o Q3=median of the second half of data
10.7+11=21.7/2=10.85
Interquartile Range (IQR)
o Distance from Q1 to Q3
o IQR=Q3-Q1
o EX: 10.85-8.3=2.55
Outlier: unusually small or large observation
1.5(IQR) Criterion: if an observation is less than Q1-1.5(IQR) or greater than
Q3+1.5(IQR) it is an outlier
Five-number summary: set of data including the minimum value, Q1, median, Q3, and
max value=BOX PLOT
o If there are outliers, the mean>median
Skewed left or right
Skewed right; 50% of data on left
Skewed left; 50% of data on right
o IQR=higher spread, the box in the box plot will be bigger
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