1. Statistics and Probability Grade 6
Mathematics
Statistics and Probability
Grade 6

2. Introduction Title: Statistics and Probabilities
Brief introduction: Being able to understand the differences in statistical variability and non statistical questions.
Subject: Mathematics
Topic: Statistical Variability
Objectives:
The students will be able to decipher the difference between a non statistical question and a statistical variability question.
The students will also be able to take the statistics and develop a set of data that can be placed into data plots (Mean, Median, Mode).
The students will be able to take the data and develop a summary of the answers they have developed.

3. Introduction Continued
Procedure:
A list of statistical variability questions will be provided as well as a list of non statistical variability questions.
The substitute will ask the students the questions and they will have to determine which ones have variability and which don’t.
After students have deciphered which type of questions are which they will collect a set of data, from within the classroom, on the questions which provide variability.
Once the data is collected the students can work together in groups of four to take their data and place it into data plots.
The students will need to make two different data plots ( out of an option of 4 different plots provided on the back of the lists from step one) with the numbers they collected.
After students have completed the three previous steps, they will need to develop a summary of all the work they have completed and how the data and plots work with the statistical variability questions.

4. Introduction Continued
Evaluation:
Before: The students already know about statistics and developing data. From this lesson they will be learning how to develop statistics with variability.
During: While this process is being taught, it will be important to make sure that the students will be able to determine the difference between non statistical variability and statistical variability.
After: To determine that the students have learned the lesson appropriately a quiz or test will be provided.
Materials:
List of questions
Plain paper for data plots
Lined paper for writing summary of lesson
Rulers

5. Questions What grade did I receive on my homework? How old am I?
Non Statistical Variability
Statistical Variability
What grade did I receive on my homework?
How old am I?
How many pets do I have?
What average grade did all my classmates including myself receive?
How old are the students in the class? What is the mode?
How many pets do my classmates and I have? What is the median?

6. Terms to Know
Mean (Average): Add together all test results and then divide it by the sum of the total number of marks there are.
Median: The median is the middle value in the list. When the totals of the list are odd, the median is the middle entry in the list after sorting the list into increasing order. When the totals are even, the median is equal to the sum of the two middle (after sorting the list into increasing order) numbers divided by two.
Mode: The mode in a list of numbers refers to the list of numbers that occur most frequently.
Hint: MODE and MOST have the same first two letters.
# 3
# 1
# 2

7. What is the class average pulled from this data?
70,70,70,75,75,80,80,80,80,80,80,85,85,85,85,85,90,90,90,95,100,100,100,100
Add all numbers together and divide by 23.
What is the answer?
88.26
87.92
88.45
MEAN (AVERAGE)
What average grade did all my classmates, including myself, receive for our exams?
Terms

8. Determine the median from the provided data.
Students:
1: 2 animals
2: 1 animal
3: 0 animals
4: 3 animals
5: 0 animals
6: 1 animal
7: 2 animals
8: 5 animals 2
9: 0 animals
10: 3 animals
11: 1 animal 1
12: 2 animals
13: 2 animals
14: 2 animals 0
15: 1 animal
16: 1 animal
17: 0 animals
18: 0 animals
19: 1 animal
20: 5 animals
21: 6 animals
22: 0 animals
23: 2 animals
MEDIAN
How many pets do my classmates and I have? What is the median number?
Terms

9. MODE Terms How old are the students in the class? What is the mode?
Determine the mode from the below data.
Students
Student 1: 11
Student 2: 12
Student 3: 12
Student 4: 12
Student 5: 12
Student 6: 11
Student 7:
Student 8: 12
Student 9: 12
Student 10:
Student 11: 11
Student 12: 12
Student 13: 12 Both
Student 14: 12
Student 15: 11
Student 16: 11
Student 17: 12
Student 18: 12
Student 19: 11
Student 20: 11
Student 21: 12
Student 22: 12
Student 23: 12
MODE
How old are the students in the class? What is the mode?
Terms

10. CORRECT!
When it all = 2030
Then 2030/ 23 = 88.26 #2

11. INCORRECT
Make sure that all numbers were added correctly and divided properly.
Don’t be discouraged!!!
TRY AGAIN!
Return

12. INCORRECT Double check that all numbers are in the correct order.
Recount the numbers to determine of it is odd or even and proceed from there.
RETRY!!!
Return

13. CORRECT!! Lining the numbers up correctly should appear like this:
0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,5,5,6
Counting the numbers you should have come up with 23 which is odd, which means that the median is in the list already above (highlighted number). #3

14. INCORRECT
The answer is not 11 nor both because there are only 9 students who are 11 and there are 14 students who are 12.
Therefore the number that is most frequent is 12.
Return

15. CORRECT!!!
There are 14 students who are 12 years old compared to 9 students who are only 11 years old.
Congratulations on determining the most frequent age in the class.
END

16. Congratulations!!! You have completed the mini quiz!
You are now able to determine the difference between a non statistical variability and a statistical variability.
You also now know how to determine the MEAN, MEDIAN, and MODE.

17. REFERENCE
Russell, By Deb. "The Law of Averages. The Mean, the Median and the Mode. Understand the Basics of Statistics." Math Tutorials, Resources, Help, Resources and Math Worksheets. Web. 09 Oct <