2. Aim: Central Tendencies Course: Alg. 2 & Trig. Aim: How do we make sense out of data? - What’s the central issue? Do Now: 39 37 34 30 25 19 16 39 29 25 19 17 18 37 33 31 20 17 17 15 44 40 35 29 24 17 15 Draw a histogram with your calculator using the following data:

3. Aim: Central Tendencies Course: Alg. 2 & Trig. Recall: Model Problem A teacher marked a set of 32 papers. The grades were as follows: 90, 85, 74, 86, 65, 62, 100, 95, 77, 82, 50, 83, 77, 93, 72, 98, 66, 45, 73, 100, 50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75. STAT  EDIT  1 STAT  CALC  1 ENTER

4. Aim: Central Tendencies Course: Alg. 2 & Trig. Mean or Average n = 32 - to find the mean of a set of n numbers, find the sum (  ) of the numbers and divide by n. our test data

5. Aim: Central Tendencies Course: Alg. 2 & Trig. Mode The value that appears most often in a set of data. 45, 50, 50, 62, 65, 66, 70, 72, 72, 73, 74, 75, 75, 77, 77, 78, 78, 80, 81, 82, 83, 83, 85, 86, 89, 90, 93, 95, 95, 98, 100, 100 Mode - 50, 72, 75, 77, 78, 83, 95, and 100 all occur twice our test data

6. Aim: Central Tendencies Course: Alg. 2 & Trig. Median when a set of data is arranged in numerical order, the middle value is called the median. 45, 50, 50, 62, 65, 66, 70, 72, 72, 73, 74, 75, 75, 77, 77, 78, 78, 80, 81, 82, 83, 83, 85, 86, 89, 90, 93, 95, 95, 98, 100, 100 Median - 78 our test data 32 numbers median is between the 16 th and 17 th number

7. Aim: Central Tendencies Course: Alg. 2 & Trig. Recall: Model Problem A teacher marked a set of 32 papers. The grades were as follows: 90, 85, 74, 86, 65, 62, 100, 95, 77, 82, 50, 83, 77, 93, 72, 98, 66, 45, 73, 100, 50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75. Mean - Median - 78 Mode - 50, 72, 75, 77, 78, 83, 95, and 100 all occur twice Modal Interval - Interval w/Median - 71 - 80 interval with greatest number of values interval in which the median of n values is located

8. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problem Mrs. Taggart bought a new car. She kept a record of the number of miles that she drove per gallon of gas for each of the first 6 times she filled the tank. Her record showed the following numbers of miles per gallon: 29, 32, 32, 33, 35, 37. Find: a) the mean b) the median c) the mode 33 32.5 32

9. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problem The ages of 25 students in a senior high school mathematics class are recorded in the frequency distribution table below. Find: a) the mean b) the median c) the mode Age in years x Frequency f 182 1711 1612 a) the mean xffx 18236 1711187 1612192

10. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problem The ages of 25 students in a senior high school mathematics class are recorded in the frequency distribution table below. Find: b) the median Age in years x Frequency F 182 1711 1612 xffx 18236 1711187 1612192 median is 13 th num. 17

11. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problem The ages of 25 students in a senior high school mathematics class are recorded in the frequency distribution table below. Find: c) the mode Age in years x Frequency f 182 1711 1612 16

12. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problem 5 baseball player weight 168, 174, 181, 195 and 182. Find the average weight. n = 5,

13. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problem Tony has marks of 75, 82, and 90. What mark must he obtain on the next test to have an average of exactly 85. 75 + 82 + 90 + t 4 = 85 247 + t 4 = 85 247 + t = 85(4) = 340 t = 93

14. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problems Express the mean of x - 1, x + 2, 2x - 3, and 4x + 6 as a binomial. n = 4 x - 1 + x + 2 + 2x - 3 + 4x + 6 4 = 8x + 4 4 = 8x 4 + 4 4 = 2x + 1 For which set of data do the mean, median, and mode all have the same value? 1) 1, 3, 3, 3, 5 2) 1, 1, 2, 5, 6 3) 1, 1, 1, 2, 54) 1, 1, 3, 5, 10 n = # being averaged,

15. Aim: Central Tendencies Course: Alg. 2 & Trig. Model Problem Write a set of numbers satisfying the conditions given in the following: 1. The mean is greater than the median. 2. The mean, median, and mode are all the same number. 3. The mode is 40 and the median is 20. 4. The group is bimodal and the mean and median are 14.

16. Aim: Central Tendencies Course: Alg. 2 & Trig.