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How do you calculate and interpret measures of center & spread?
Notes 13.2
Measures of Center
& Spread
Warm-up
Classify each question from
yesterday’s survey as
qualitative or quantitative.
How do you calculate and interpret measures of center & spread?
I. Summation Notation:
A. Also called sigma-notation
b
B.
x
i a
i
, the sum of x-sub-i’s as i goes
from a to b. xa  x f  ...  xb 
How do you calculate and interpret measures of center & spread?
II. Measures of Center:
A. Mean
- Average of a set of numbers
n
-
x
i 1
n
i
B. Median – Middle value of a set of data
listed in increasing or decreasing order
C. Mode – Most common item in a set of
data
How do you calculate and interpret measures of center & spread?
II.
Examples for Measures of Center:
1. Compile the data on how many people
live in your home. Find the mean,
median, and mode for this data.
2
3
4
5
6
7
8
9
10
11
12
How do you calculate and interpret measures of center & spread?
III. Measures of Spread:
A. Standard Deviation
–
–
–
Measures the average distance of a data
element from the mean.
Normally pair with mean.
Best used when data is symmetric
B. Variance – Square of Variance
C. Range – difference between the
maximum and minimum data values.
How do you calculate and interpret measures of center & spread?
III. Measures of Spread:
D. Interquartile Range – IQR
–
–
–
–
Normally paired with median
Measure of variability that is resistant to
extreme values
Difference between 1st quartile and 3rd
quartile
Used to find outliers
How do you calculate and interpret measures of center & spread?
III. Finding Outliers
• Upper fence
– Any number above Q3 + 1.5 (IQR)
• Lower fence
– Any number below Q1 – 1.5 (IQR)
• Always check the context of a
problem when checking for outliers.
How do you calculate and interpret measures of center & spread?
III.Examples for Spread:
2. Compile the data on how many people
live in your home. Find the standard
deviation, range, and IQR.
2
3
4
5
6
7
8
9
10
11
12
How do you calculate and interpret measures of center & spread?
IV. 5 Number Summary & Box Plots
A. Quartiles:
1. Values that divide an ordered set into
four subsets of approximately equal
size
2. Steps
• Place data in order
• Find the median (second quartile)
• Find half way between the minimum &
median (first quartile)
• Find half way between the maximum &
median (third quartile)
How do you calculate and interpret measures of center & spread?
IV. 5 Number Summary & Box Plots
B. Box Plots (Box-and-whisker plot):
1. Draw a number line that includes the minimum &
maximum values
2. Use the first quartile, median & 3rd quartile to
create the box
3. Place a dot at the minimum & maximum to create
the whiskers.
4. Title and label plot.
How do you calculate and interpret measures of center & spread?
IV. Examples:
3. Compile the data on how many people
live in your home. Find Five-Number
Summary & Create a box plot.
2
3
4
5
6
7
8
9
10
11
12
How do you calculate and interpret measures of center & spread?
Practice:
Consider another type of quantitative data
from our survey.
• Find the measures of center and spread.
Which of these best describes this data?
• Are there any outliers?
• Create a box plot to illustrate this data.
How do you calculate and interpret measures of center & spread?
Homework:
Pages 862-863
#2,6,22,26,30,34,38,40,42