Statistics and Probability Grade 6 Mathematics Statistics and Probability Grade 6

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.

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.

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

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?

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

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

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

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: 11 11 Student 8: 12 Student 9: 12 Student 10: 11 12 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

CORRECT! When 70+70+70+75+75+80+80+80+80+80+80+85+85+85+85+85+90+90+90+95+100+100+100+100 it all = 2030 Then 2030/ 23 = 88.26 #2

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

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

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

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

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

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.

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. 2010. <http://math.about.com/od/statistics/a/MeanMedian.htm>.