Part I: Numbers and Operations Lesson 3: Sets and Series

Set A collection of distinct, symbols unordered objects The members of the set should be distinct. (not be repeated) The members of the set should be well-defined. (well-explained)

Set Write as {1,8,3,14,5}, {1,2,3,4,…..}, {all even numbers}, {a, t, w, o, p}, {desk, chair, bookshelf, printer} A={1} and B={1,2,3}, then A B, which means A is a subset of B {1, 2, 3}={3, 2, 1}

Sequence 1, 4, 7, 10, 13, 16, 19….; -2, 0, 2, 4, 6, 8, …; 1+3=4, 4+3=7, 7+3=10, 10+3=13… -2+2=0, 0+2=2, 2+2=4, ….. Every number equals the previous one plus a fixed number an=an-1 + m (n=2,3,4,5,…)

Fibonacci Sequence Sequence 0, 1, 1, 2, 3, 5, 8, 13,…. 0+1=1, 1+1=2, 2+3=5, 5+8=13 an=an-2+an-1 (n=3,4,5,….)

Mean The arithmetic average of all numbers The sum of all given elements divided by the total number of elements Formula: (a1+a2+a3+…+an)/n 1, 3, 6, 9, 11; the mean M=(1+3+6+9+11)/5=6

Median The middle value in a list of numbers If there are odd numbers in the list, after sorting them into increasing/decreasing order, the median is the middle entry If there are even numbers in the list, after sorting them into increasing/decreasing order, the median is the sum of the middle two divided by 2

Median Odd number list: 1, 3, 6, 7, 9, median is 6 Even number list: 2, 5, 7, 8, median is (5+7)/2=6

Mode The number/numbers that occur/occurs the most frequent in a list of numbers 3, 5, 2, 5, 6, 4, 7, 3, 5, 6, 9, 5, 10, 5 Put them in order: 2, 3, 3, 4, 5, 5, 5, 5, 5, 6, 6, 7, 9, 10 The mode is 5 which occurs 5 times

Exercises 1.What is the mean of 9, 13, 6, 4? A. 3 B. 10 C. 8 D. 12

Exercises 2. What is the median of 4, 8, 2, 7, 5, 3? A. 4 B. 5 C. 6 D. 4.5

Exercises 3. What is the possible value of the next number in 2, 5, 8, 11, 14, ? A. 17 B. 15 C. 18 D. 16

Exercises 4. There are 16 students in four math groups. Their scores are listed below. You would like to join the group with the highest mean score. Which on is it? A. A B. B C. C D. D A B C D S1 68 72 77 80 S2 88 73 85 S3 66 90 71 S4 84 89 69

Do it again

Do it again

Do it again

Do it again

Excellent job! (9+13+6+4)/4 =8

Wonderful! Put them in order: 2,3,4,5,7,8 The median is (4+5)/2=4.5

Brilliant! 3 is the fixed number that add to the previous one. So, the next one is 14+3=17

You are great! Group B has the highest mean 83.5

References http://math.wikia.com/wiki/Set http://math.about.com/od/statistics/a/MeanMedian.htm