`
`
`
Numerically
`
Order:
4 4 4 5 5 5 6 6 6 6 7 8 8 10 10 11 11 12 15 15 16 33 38
Med =
`
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
Numeric description of the distribution
1. Minimum
2. 1st Quartile (Q1) – Middle number of the
bottom half of the data
3. Median
4. 3rd Quartile (Q3) – Middle number of the top
half of the data
5. Maximum
`
`
Put data in order
`
Range = Max – Min
4 4 4 5 5 5 6 6 6 6 7 8 8 10 10 11 11 12 15 15 16 33 38
Min = 4
`
Q1 = 5
Med = 8
Q3 = 12
Interquartile Range
` IQR = Q3 – Q1
Max = 38
Graphical display of 5 number summary
`
`
y
`
x
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
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)
`
`
y
If outliers are present the whisker extends to
the last value not an outlier
The outlier is marked with an x, box, or point
Always choose the modified boxplot.
x
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Here is the relative frequency histogram from
the list CHOLA, the cholesterol levels of a
sample of smokers. Describe the distribution:
Here is the 5# summary for the data. Is the
maximum an outlier?
min = 155
Q1 = 211
med = 230
Q3 = 267
max = 351
Here is the 5# summary for the data in
STELD(percent of people 65+ in each state).
min = 7
Q1 = 12.2
med = 13
Q3 = 13.6
max = 17
Using the 1.5 rule check for outliers.
x
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.