1. Notes 13.2 Measures of Center & Spread
How do you calculate and interpret measures of center & spread?
Notes Measures of Center & Spread
Warm-up
Classify each question from yesterday’s survey as qualitative or quantitative.

3. I. Summation Notation: Also called sigma-notation
How do you calculate and interpret measures of center & spread?
I. Summation Notation:
Also called sigma-notation
, the sum of x-sub-i’s as i goes
from a to b.

4. II. Measures of Center: Mean
How do you calculate and interpret measures of center & spread?
II. Measures of Center:
Mean
- Average of a set of numbers -
Median – Middle value of a set of data listed in increasing or decreasing order
Mode – Most common item in a set of data

5. II. Examples for Measures of Center:
How do you calculate and interpret measures of center & spread?
II. Examples for Measures of Center:
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

6. III. Measures of Spread:
How do you calculate and interpret measures of center & spread?
III. Measures of Spread:
Standard Deviation
Measures the average distance of a data element from the mean.
Normally pair with mean.
Best used when data is symmetric
Variance – Square of Variance
Range – difference between the maximum and minimum data values.

7. III. Measures of Spread:
How do you calculate and interpret measures of center & spread?
III. Measures of Spread:
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

8. III. Finding Outliers Upper fence Lower fence
How do you calculate and interpret measures of center & spread?
III. Finding Outliers
Upper fence
Any number above Q (IQR)
Lower fence
Any number below Q1 – 1.5 (IQR)
Always check the context of a problem when checking for outliers.

9. III. Examples for Spread:
How do you calculate and interpret measures of center & spread?
III. Examples for Spread:
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

10. IV. 5 Number Summary & Box Plots
How do you calculate and interpret measures of center & spread?
IV. 5 Number Summary & Box Plots
Quartiles:
Values that divide an ordered set into four subsets of approximately equal size
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)

11. IV. 5 Number Summary & Box Plots
How do you calculate and interpret measures of center & spread?
IV. 5 Number Summary & Box Plots
Box Plots (Box-and-whisker plot):
Draw a number line that includes the minimum & maximum values
Use the first quartile, median & 3rd quartile to create the box
Place a dot at the minimum & maximum to create the whiskers.
Title and label plot.

12. 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

13. Practice: Consider another type of quantitative data from our survey.
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.

14. How do you calculate and interpret measures of center & spread?
Homework:
Pages #2,6,22,26,30,34,38,40,42