1. Describing Distributions with Numbers
Section 1.2

2. Two Ways to Measure the Center
Mean
Median
Mean—add up all the observations and divide by the number of observations you have
Mean is not resistant to extreme values
Median—arrange all observations in order from smallest to largest
If the number of observations is odd, it’s the middle value
If the number of observations is even, it’s the mean of the two center values
Median is resistant to extreme values

3. Ways to Measure the Spread
Range
Quartiles
Standard Deviation
Range—highest value versus lowest
Q1—median of observations to the left of the median
Q3—median of observations to the right of the median

4. IQR Interquartile Range Distance between the first and third quartiles
IQR = Q3 – Q1
IQR--Spread of the middle half of data

5. Identifying Outliers Multiply the IQR by 1.5
An observation is an outlier if it falls IQR(1.5) above the third quartile or below the first quartile

6. Five Number Summary Used to create a boxplot/modified boxplot
Minimum, Q1, Median, Q3, Maximum
Used to create a boxplot/modified boxplot
Use for skewed distributions or distributions with strong outliers

7. Variance
The average of the squares of the deviations of the observations from the mean

8. Degrees of Freedom
n – 1
n is the number of observations in your data set

9. Linear Transformation
Changes the original variable x into the new variable xnew
Xnew = a + bx
a shifts values of x up or down (changes center, not spread)
b changes the size of the unit of measurement (changes center and spread)
Does not change shape