1. MEAN AND RANGE

2. 6PS1.1 Compute the range, mean, median, and mode of data sets Objective: Understand what the mean and range of a data set stand for Learning target: Answer at least 3 of the 4 mean and range questions correctly on the exit ticket.

3. What is a data set? A group of numbers or values. Example: { 72, 65, 78, 67, 70 } could be a data set for the temperatures last week. Each number is one day’s temperature. Example: Bob polls his classmates about what their favorite number is. His data set might be { 4, 2, 3.14, 9, 0, -3 } where each number is one person’s response.

4. What is the mean (also called average) of a data set? If you take from the bigger numbers and give them to the smaller numbers until they are all equal, that number that they end up at is called the mean.

5. How do we calculate the mean of a data set? Let’s figure it out with an activity.

6. Calculating Mean Activity I will give each person in the group some pieces of paper. Each person’s amount of scraps is like their number in the data set. Your group will find the mean of your data set. This means you will find out how many pieces of paper each of you needs to have in order for all of you to have the same amount. Move around the pieces among the people in your group until everyone has the same amount.

7. Discussion What strategy did your group use in order to get everyone to have the same amount of pieces?

8. Cards You and your friends just finished a card game and each of you has a different amount of cards. When the new game starts, each of you needs to have an equal amount of cards. What do you do to make sure each person has the same amount of cards?

9. Cards First, everyone would combine their cards into one pile, the deck. What operation does this represent? All the numbers in the data set are being added together. The sum is the size of the deck of cards. Then, someone would deal out the cards into equal groups. What operation does this represent? The deck of cards (sum) is being divided into groups, one group per player.

10. How do we calculate the mean of a data set? Add up all of the numbers. Remember, this is like combining everyone’s cards into one deck. Divide the sum by the amount of numbers there were. Remember, this is like dealing out the deck to however many players there are.

11. What is the mean of {4, 10, 1}? What is the mean of {7, 9, 0, 8} 4 + 10 + 1 = 15 Since there were 3 numbers, divide the sum by 3: 15 ÷ 3 = 5 7 + 9 + 0 + 8 = 24 24 ÷ 4 = 6 0 is still a number so include it when you’re counting numbers to see what to divide by

12. The char below shows how many hours Jill worked each day last week. How many hours did she work per day on average? 6 + 7 + 8 + 2 + 4 = 27 27 ÷ 5 = 5.4 MondayTuesdayWednesdayThursdayFriday # hours worked 6 7 8 2 4

13. What is the range of a set of data? The difference between the greatest and least numbers. Subtract these two numbers to find the range. This is useful for knowing how different the numbers in a data set are. Example: In Town A, the temperatures were 70, 70, 70. In Town B, the temperatures were 50, 90, and 70. Both have the same mean temperature but Town B experienced a greater range of temperatures.

14. What is the range of this set: {11, 25, 9, 14, 37, 10} 37 – 9 = 28

15. The char below shows how many hours Jill worked each day last week. What is the range of her hours per day? 8 – 2 = 6 MondayTuesdayWednesdayThursdayFriday # hours worked 6 7 8 2 4

16. Direct Station We will do problems that show how the mean is used in real-life, such as in sports and grades.

17. Collaborative Station You and your table will create a set of data by each answering the question. Then, you will all calculate the mean and range of your data set. Example: How old are you? Group members’ answers are 11, 11, 12, and 12. They write down the data set {11, 11, 12, 12} The group calculates the range is 12 – 11 = 1 and the mean:11 + 11 + 12 + 12 = 46, so 46 ÷ 4 = 11.5

18. Independent Station You will begin ST Math’s unit on mean. Remember, the definition of mean is the amount each data point would be if they were all equalized.