1. Statistics and Probability
MATH th Exam Review
Statistics and Probability

2. Problem Solving – Polya’s 4 Steps
Understand the problem
What does this mean?
How do you understand?
Devise a plan
What goes into this step?
Why is it important?
Carry out the plan
What happens here?
What belongs in this step?
Look back
What does this step imply?
How do you show you did this?

3. Problem Solving Polya’s 4 Steps Which step is most important?
Understand the problem
Devise a plan
Carry out the problem
Look back
Which step is most important?
Why is the order important?
How has learning problem solving skills helped you in this or another course?

4. 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

5. 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

6. 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

7. 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

8. 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

9. Statistics Measures of Central Tendency Measures of dispersion Mean
Median
Mode
Measures of dispersion
Range

10. Statistics Experimental Error
Absolute value of the difference between an experimental or estimated value and a theoretical or known value divided by the theoretical or known value

11. Statistics Types of Data
Interval/ratio – temperatures, prices, test scores, etc.
Ordinal – low, medium, high
Nominal – red, blue, green
Discrete – people, keys, desks, etc.
Ordinal
Nominal
Interval/ratio
Continuous - temperatures, prices, test scores, etc.

12. 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

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

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

15. 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 =

16. 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

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

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

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

20. 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

21. 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

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

23. 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}

24. Probability Experiment Examples Cardinality of Sample Spaces
One coin tossed: S = {H, T}
n(S) = 21 = 2
Two coins tossed: S = {HH, HT, TH, TT}
n(S) = 22 = 4
One die rolled: S = {1, 2, 3, 4, 5, 6}
n(S) = 61 = 6
One coin tossed and one die rolled: S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
n(S) = 21 x 61 = 12

25. 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

26. 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

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

28. 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