1. Warm Up # 3: Answer each question to the best of your knowledge.
What is univariate data?
What is the purpose of a back to back bar graph?
How is a histogram different from a bar graph?
What is an interval?
What are class mark?
What is a frequency distribution?
What are the three measures of central tendency?
How do you find the mean of a frequency distribution table?
What does a stem-n-leaf plot best illustrate?

2. Measures of Variability
Statistics
Measures of Variability

3. Essential Question:
What does the measure of variability indicate about a set of data?

4. Introduction to Links:

5. Lets Digest:
How well did the mean, median, or mode represent the data set we just looked at?
What about these two:
A = {35, 40, 45}
B = {10, 40, 70}
Both have the same mean but in one the numbers are “farther” from the mean than in the other

6. Measures of Variability
Describe how much a set of data varies
Consistency
How strongly data related
Example
A = {35, 40, 45}
B = {10, 40, 70}
The mean is not accurate because the 2nd set has more variability.

7. Main ways to represent variability:
Range
Box and
Whisker
Plot
Standard
Deviation
Practice!

8. Range
Difference between the greatest number and the least number in a set.
What if I told you a set of data has a range of 127, is that good or bad?
You don’t know unless you know more about the data set.

9. Box and Whisker Plots: Graphical representation of variation
Similar to how a Histogram lets us “see” what the average value is without actually knowing what it is.

10. Box and Whisker Plots: Median (Q2) Q1 – Median of the lower half
Q3 – Median of the upper half
Outlier
Extreme Value (Lower)
EV (Upper)

11. Box and Whisker Plot Use to illustrate variability not quantity
Show your quartile, min, max, and outliers
Your Q1, Q2, Q3 are your quartile
Interquartile Range (IQR):
Q3 – Q1
Semi-interquartile:
IQR/2

12. Calorie’s from 20 popular cereals:50 90
100
110
120
125
130
140
155
165
200
210
220
250
260
265
270
300

13. Calculating Outliers Find your IQR Take your IQR*1.5 Q1 – 1.5IQR
A number is an outliers if it is below this
Q IQR
A number is an outliers if it is above this

14. Now you try:
506
583
612
102
789
881
412
457
814
826
First organize the data in increasing order
Find the median
Split the data into two sets and find the median of each
See if there are any outliers
Plot the extreme values

15. Standard Deviation
Numerical Method to show Variability – we see more about Standard Deviation later
Describe how much items vary from the mean

16. Calculating Standard Deviation
Find the mean of a given data
Subtract the mean from each individual data
Then square each result
Add all together
Then divided by how many they are
Take the square root of that number.

17. Calorie’s from 20 popular cereals:50 90
100
110
120
125
130
140
155
165
200
210
220
250
260
265
270
300

18. Now you try:
506
583
612
102
789
881
412
457
814
826

19. Revisiting the EQ:
What does the measure of variability indicate about a set of data?

20. Practice: Link Sheets