Numerically

Mean: arithmetic average, add all observations together and divide by the number of observations.

If there are n observations which are labeled as ;The mean is

Read as “x bar” Must be written with the bar!!!!

1 2, ,..., nx x x

1

n

ii

x x

25n27 4 14 9

25x

9.92x

the middle obsevation Arrange the data in order from least to

greatest If an odd number of obs. find the middle

number If an even number of obs. find the average

of the middle two numbers

Order:2 2 3 4 5 5 6 6 7 7 7 7 7 8 9 9 9 10 11 12 14 16 19 27 35

Med =

If the distribution is symmetric the mean the median will be approximately the same

If the distribution is skewed to the left, the mean will be less than the median

If the distribution is skewed to the right, the mean will be higher than the median

The mean is affected by outliers and the median is resistant to outliers

When the data is symmetric use the mean When the data is skewed use the median

Numeric description of the distribution Minimum 1st Quartile (Q1) – Middle number of the

bottom half of the data Median 3rd Quartile (Q3) – Middle number of the top

half of the data Maximum

Put data in order2 2 3 4 5 5 6 6 7 7 7 7 7 8 9 9 9 10 11 12 14 16 19 27 35

Min = 2 Q1 = 5.5 Med = 7 Q3 = 11.5 Max = 35

Graphical display of 5 number summary

Range = Max – Min  

Interquartile Range IQR = Q3 – Q1

Any observation below the Lower Fence (LF) or above the Upper Fence (UF) is considered an outlier

LF = Q1 – 1.5(IQR) UF = Q3 + 1.5(IQR)

If outliers are present the whisker extends to the last value not an outlier

The outlier is marked with an x, box, or point