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

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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