1. Good research questions
Review
Good research questions

2. Create a good research question
Age
Income
Health
Education
Using two of the concepts from above create a good research question. Explain the criteria as it pertains to your question.
What is the average income of high school graduates?
Population: High School graduate
Variable: Income
Numerical Characteristic: Average income

3. Review
Mean as a balance point

4. Mean as a balance point

5. Mean as a balance point

6. Mean as a balance point

7. Mean as a balance point

9. Which is your favorite
season?
Fall
Spring ✿
Summer R
Winter T

10. Which is your favorite
season?
Fall
Spring ✿
Summer R
Winter T

11. Brainology
Do you think the description matches the way you think and feel about school work?
Which parts are true?
Which parts are not?

12. Which is your favorite main subject?
Science
Language Arts
Social Studies
Math

13. Which is your favorite main subject?
Science
Language Arts
Social Studies
Math

14. Module 7
What where the big ideas from Module 7 (dot plots and histograms). Discuss with your group and write one idea of the board.

15. What continent would you most like to visit?

16. Africa

17. Europe

18. Asia

19. Australia

20. What continent would you most like to visit?
Africa
Asia
Europe
Australia

21. Module 8
Discuss module 8 with your group. What questions do you still have. Write them on the board.

22. Mean What are three other words for mean?
What does it mean as mean at the balance point?
Practice:
Find the mean of the following data. Then find the find the sum of the distance from the mean.
5, 10 16, 6, 55, 22

23. Which would be hardest to live without?
cell
phone TV
ipod
video
games

24. Which would be hardest to live without?
cell
phone TV
ipod
video
games

25. What’s the age?
This is your group you will work with for the next activity.
Find a seat

26. Interquartile Range and Boxplots
Module 9
Math 075 Summer 2015

27. Variability Depends on how we measure variability:
One way is to find the range:
Maximum Value – minimum Value
But what if the data sets have the same range?
Lets look at the distribution of the data.

28. Variability about the median
Quartiles: Divides the data into four equal parts. (25% of the data will be in each quartile)
Some quartiles have more variability than others.
We find the Interquartile range: Q3 – Q1

29. The 5 Number Summary The five number summary consist of :
The median ( 2nd quartile)
The 1st quartile
The 3rd quartile
The maximum value in a data set
The minimum value in a data set

30. The 5 Number Summary
Step 1 - take the set of numbers given…
34, 18, 100, 27, 54, 52, 93, 59, 61, 87, 68, 85, 78, 82, 91
Place the numbers in order from least to greatest:
18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100

31. 68 is the median of this data set.
The 5 Number Summary
Step 2 - Find the median.
Remember, the median is the middle value in a data set.
18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100
68 is the median of this data set.

32. The 5 Number Summary Step 3 – Find the lower quartile.
The lower quartile is the median of the data set to the left of 68.
(18, 27, 34, 52, 54, 59, 61,) 68, 78, 82, 85, 87, 91, 93, 100
52 is the lower quartile

33. The 5 Number Summary Step 4 – Find the upper quartile.
The upper quartile is the median of the data set to the right of 68.
18, 27, 34, 52, 54, 59, 61, 68, (78, 82, 85, 87, 91, 93, 100)
87 is the upper quartile

34. 18 is the minimum and 100 is the maximum.
The 5 Number Summary
Step 5 – Find the maximum and minimum values in the set.
The maximum is the greatest value in the data set.
The minimum is the least value in the data set.
18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100
18 is the minimum and 100 is the maximum.

35. The 5 Number Summary Step 5 – Find the inter-quartile range (IQR).
The inter-quartile (IQR) range is the difference between the upper and lower quartiles.
Upper Quartile = 87
Lower Quartile = 52
87 – 52 = 35
35 = IQR
Looking at the middle 50% of the data

36. The 5 Number Summary Organize the 5 number summary Median – 68
Lower Quartile – 52
Upper Quartile – 87
Max – 100
Min – 18

37. What about outliers?
Boxplots are the only graphical representation where we specifically define an outlier
Potential outliers are values that are more than 1.5 IQRs from Q1 or Q3
IQR x 1.5; add that product to Q3; any value(s) beyond that point is an outlier to the right
Q1; any value(s) beyond that point is an outlier to the left

38. Siblings data... Using Stat Crunch, calculate descriptive statistics
Let’s calculate (by hand) to see if we have any outliers
Q3 – Q1 = IQR
IQR x 1.5; add this product to Q3; are there any values
in our data set beyond this point to the right?
IQR x 1.5; subtract product from Q1; are there any values in our data set beyond this point to the left?
Now use Stat Crunch to create a boxplot; are our calculations confirmed
with our boxplot?

39. Box and Whisker Diagrams. Anatomy of a Box and Whisker Diagram.
Lower Quartile
Upper Quartile
Lowest Value
Median
Highest Value
Box
Whisker 4 5 6 7 8 9 10 11 12
Box Plots

40. Graphing The Data
Notice, the Box includes the lower quartile, median, and upper quartile.
The Whiskers extend from the Box to the max and min.

41. Do you know your geography?
Look at the slip of paper I gave you. With out talking to anyone answer the questions to the best of your ability.
Now find your group according to the first question on your paper.
Line up in order of your population estimate
Find the 5-number summary
Determine if there is any outliers
Draw one boxplot for each group on the board
In your groups find one observation about the two box plots
Have students do the 5 number summary.

42. Do you know your geography?
The actual population is 13646
How close was your estimate?
Which group did a better job?
How can you tell?
Why do you think one group did better than the other?
Have students do the 5 number summary.

43. Interpreting the Box Plot:
Study your Box and Whisker Plot to determine what it is telling you. Make a statement about what it is saying, then support the statement with facts from your graph.

44. You should include the following in your interpretation:
Range or spread of the data and what it means to your graph
Quartiles—compare them. What are they telling you about the data?
Median- this is an important part of the graph, and should be an important part of the interpretation.
Percentages should be used to interpret the data, where relevant.

45. Analyzing The Graph
The data values found inside the box represent the middle half ( 50%) of the data.
The line segment inside the box represents the median

46. Your turn...
In pairs, choose a set of data from the Math 075 spreadsheet that is skewed (to left or right); you probably won’t know if the data is skewed until you copy and paste into Stat Crunch and create a graph
Create a box plot; print out; put your names on it
Label (on the graph) the 5-number summary (with arrows pointing to each value on the graph)
Analyze through SOCS (which measure of central tendency should you use? Which measure of spread should you use?); be sure you show your work to justify that a point/points are outliers
Now, using the same data, create a histogram. What characteristics of the data does the histogram show that the box plot does not?

47. Project #2
You now have time to work on this project. You will need to present this project on Thursday

48. Homework
Read OLI 41-44
Check point for Module 8
Journal #3 Brainology