Transcript Chapter 2.5 Notes

Warm Up
Find the median of the following data set. Car
accidents on Main and First street during the
past 7 years.
24 10
14 35 8 41 88
Chapter 2.5 Notes
Measures of Position
Fractiles
Fractiles are numbers that partition or divide an
ordered data set into equal parts. There are a
lot of different fractiles.
Quartiles
Quartiles are fractiles that partition the data
sets into 4 equal parts. The three quartiles are
Q1, Q2 and Q3.
1 2 2 2 2 3 5 5 5 7 9 9 9 9 15
Q2
To find Q2 you just have to find the median of
the data set
Q2 = 5
To find Q1 take the first half of the data and find
the median
1 2 2 2 2 3 5
Q1
Q1=2
To find Q3 you must take the second half of the
data and find the median of that.
5 7 9 9 9 9 15
Q3
Q3=9
1 2 2 2 2 3 5 5 5 7 9 9 9 9 15
Q1
Q2
Q3
Box and Whisker Plot
Min = 1
Min
Q1 = 2
Q2 = 5
Q3 = 9
Max = 15
Max
Example 1
Find Q1, Q2 and Q3 and construct a box and
whisker plot.
6 4 7 10 11 14 15 20 4 8
Inter-quartile Range
This calculates the range of the box in the box
and whisker plot.
IQR = Q3 – Q1
Warm Up
Create a box and whisker plot for the following
data set. Amount of money made per hour by
9 individuals
$11.25
$12.30
$18.00
$9.50
$16.75
$10.75
$42.25
$24.80
$62.85
Types of fractiles
Quartiles : Divide data into 4 equal pieces
Deciles: Divide data into 10 equal pieces
Percentiles : Divide data into 100 equal pieces
Standard Score/Z-Score
- A z-score can be negative, positive or zero.
- Z-score represents the number of standard
deviations a given value x falls from the mean.
z = value – mean_____ = x - µ
Standard Deviation
σ
Page 92 for more info
Example 1
X = 15
µ = 12
σ=2
Example 1
X = 15
µ = 12
Z = 15 – 12 = 3
2
2
= 1.5
σ=2
Example 2
x = 8.2
µ = 25.3
σ = 7.5