1. MATH 2160 4 th Exam Review Statistics and Probability

2. Problem Solving Polya’s 4 Steps –Understand the problem –Devise a plan –Carry out the problem –Look back

3. Problem Solving Strategies for Problem Solving –Make a chart or table –Draw a picture or diagram –Guess, test, and revise –Form an algebraic model –Look for a pattern –Try a simpler version of the problem –Work backward –Restate the problem a different way –Eliminate impossible situations –Use reasoning

4. Statistics Mean –Most widely used measure of central tendency –Arithmetic mean or average –Sum the terms and divide by the number of terms to get the mean –Good for weights, test scores, and prices –Effected by extreme values –Gives equal weight to the value of each measurement or

5. Statistics Median –Put the data in order first –Odd number of data points choose the middle term –Even number of data points take the average of the middle two terms –Used when extraordinarily high or low numbers are included in the data set instead of mean –Can be considered to be a positional average

6. Statistics Mode –The mode occurs most often. If every measurement occurs with equal frequency, then there is no mode. If the two most common measurements occur with the same frequency, the set of data is bimodal. It may be the case that there are three or more modes. –Used when the most common measurement is desired –Finding the best tasting pizza in town

7. Statistics Range –The difference of the highest and lowest terms –Highest – lowest = range –Radically effected by a single extreme value –Most widely used measure of dispersion

8. Statistics Line Plot –Useful for organizing data during data collection –Categories must be distinct and cannot overlap –Not beneficial to use with large data sets

9. Statistics Bar graph –Another way of representing data from a frequency line plot –More convenient when frequencies are large

10. Statistics Line graph –Sometimes does a better job of showing fluctuation in data and emphasizing changes –Uses and reports same information as bar graph

11. Examples Test scores: 89, 73, 71, 46, 83, 67, 83, 74, 76, 79, 81, 84, 105, 84, 85, 99, 48, 74, 60, 83, 75, 75, 82, 55, 76 Mean= Sum of scores/Number of scores = 1906/25 = 76.25

12. Examples Test scores: 46, 48, 55, 60, 67, 71, 73, 74, 74, 75, 75, 76, 76, 79, 81, 82, 83, 83, 83, 84, 84, 85, 89, 99, 105 Median = 76 Mode = 83 Range = 105 – 46 = 59

13. Examples Keys in Pockets: 1, 2, 2, 3, 5, 6, 8, 5, 2, 2, 4, 1, 1, 3, 5 Line Plot

14. Examples Keys in Pockets: 1, 2, 2, 3, 5, 6, 8, 5, 2, 2, 4, 1, 1, 3, 5 Bar Graph

15. Examples Keys in Pockets: 1, 2, 2, 3, 5, 6, 8, 5, 2, 2, 4, 1, 1, 3, 5 Line Graph

16. Probability Sample space – ALL possible outcomes Experiment – an observable situation Outcome – result of an experiment Event – subset of the sample space Probability – chance of something happening Cardinality – number of elements in a set

17. Probability 0  P(E)  1 P(  ) = 0 P(E) = 0 means the event can NEVER happen P(E) = 1 means the event will ALWAYS happen

18. Probability P(E’) is the compliment of an event P(E) + P(E’) = 1 P(E’) = 1 – P(E)

19. Probability Experiment Examples –Sample Spaces One coin tossed: S = {H, T} Two coins tossed: S = {HH, HT, TH, TT} One die rolled: S = {1, 2, 3, 4, 5, 6} One coin tossed and one die rolled: S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

20. Probability Experiment Examples –Cardinality of Sample Spaces One coin tossed: S = {H, T} –n(S) = 2 1 = 2 Two coins tossed: S = {HH, HT, TH, TT} –n(S) = 2 2 = 4 One die rolled: S = {1, 2, 3, 4, 5, 6} –n(S) = 6 1 = 6 One coin tossed and one die rolled: S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6} –n(S) = 2 1 x 6 1 = 12

21. Probability Probability of Events –What is the probability of choosing a prime number from the set of digits? S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} E = {2, 3, 5, 7} n(S) = 10 and n(E) = 4 P(E) = n(E)/n(S) = 4/10 = 2/5 = 0.4 The probability of choosing a prime number from the set of digits is 0.4

22. Probability Probability of Events –What is the probability of NOT choosing a prime number from the set of digits? S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} E = {2, 3, 5, 7} n(S) = 10 and n(E) = 4 P(E) = n(E)/n(S) = 4/10 = 2/5 = 0.4 P(E’) = 1 – P(E) = 1 – 0.4 = 0.6 The probability of NOT choosing a prime number from the set of digits is 0.6

23. I think you all will probability pass this test without any trouble!! Just like puttin’ money in the bank!!!

24. Test Taking Tips Get a good nights rest before the exam Prepare materials for exam in advance (scratch paper, pencil, and calculator) Read questions carefully and ask if you have a question DURING the exam Remember: If you are prepared, you need not fear