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

2. 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)

3. 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}

4. 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,…)

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,….)

6. 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=( )/5=6

7. 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

8. 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

9. 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

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

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

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

13. 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

14. Do it
again

15. Do it
again

16. Do it
again

17. Do it
again

18. Excellent job!
( )/4 =8

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

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

21. You are great!
Group B has the highest
mean 83.5

22. References http://math.wikia.com/wiki/Set