Chapter 3: Displaying and Comparing Quantitative Data Flashcards
How To Describe A Distribution Of Quantitative Data
CUSS
Center
Unusual features (outliers, gaps, clusters)
Shape
Spread
(use -ly words)
BS
Be
Specific
(context)
Symmetric
Approx. equal on both sides
Skewed Left
“Tail” on left; “bump” on right
Skewed Right
“Tail” on right; “bump” on left
Unimodal
One “bump”
Bimodal
Two “bumps”
Uniform
Equal across all values
Mean
Sum of all the data values divided by the number of values
Median
Middle value of an ordered data set (odd number of values) or average of two middle values of an ordered data set (even number of values)
First Quartile (Q1)
Median of the first half of the ordered data set
Third Quartile (Q3)
Median of the second half of the ordered data set
Five-Number Summary
Minimum, Q1, Median, Q3, Maximum
Range
Difference between the maximum value and minimum value (max-min)
Interquartile Range (IQR)
Difference between the third and first quartiles (Q3-Q1)
Standard Deviation
Typical distance that each value is away from the mean (x̄). The square of standard deviation is the variance
How To Determine Outliers
- A value more than 1.5 IQR below the Q1 and more than 1.5 IQR above the Q3
- A value located 2 or more standard deviations above, or below the mean
Which Summary Statistics To Use For Skewed Vs. Symmetric Distributions
Skewed: median and IQR (resistant to outliers)
Symmetric: mean and range (non-resistant to outliers)
Mean Compared To Median For Different Skews Of Distributions
Skewed right: mean > median
Symmetric: mean=median
Skewed left: mean < median
