Probability+&+Statistics+0910

=<"[**Emily Gross - Notes** **= =** **Erica Little - video, notes (intro to probability)** **= =** **Kirsten Lyons - real life examples** **= =** **Dylan Horne - pictures/links** **= =** **Sarah Lehman- Sample Problems** **= =** **Carly McGlade- answer page link** Measures of Central Tendency ** Mode ** - It’s the value that occurs most frequently. If more than one number repeats multiple times then list each number. If no number repeats, then there is no mode.Sample- What is the mode in the data set of 9, 7, 13, 4, 4, 6, 5, 10, 4, 8, 9?Answer = 4, because it appears more than any other number in the set.[[image:Mode.jpg width="280" height="216"]** Median- ** central value of the data. When given a median there is an equal number of values above and below. To find the median list all the data from largest to smallest and begin crossing one number off each end to find the middle value.Sample- What is the median of the data set of 7, 8, 13, 2, 1, 4, 9, 11, 5?Answer = 7; First you have to put the number set in order...1, 2, 4, 5, 7, 8, 9, 11, 13, then find the median...[[image:math_mean_median.gif width="296" height="203"]]** Mean -** An average that uses the exact value. To find the mean add up all the numbers in the data and then divide that number by the number of numbers in the data.Sample- What is the mean of the data set of 6, 5, 8, 9, 2, 14, 15, 6, 3? Answer = 7.6

Samplings and Survey’s ** Survey- ** deduces facts about a large population by asking a select few. ** Sampling ** - Selecting a sample that is representative of the entire population ** Leading Questions - ** create a bias for a certain result ** Random sampling - ** best type of sampling, people randomly samples with no pattern ** Stratified sampling - ** a form of random sampling that divides the population into groups called strata that share a common characteristic. ** Systematic sampling - ** a way of questioning in a sequential or numerical order ** Convenience sampling ** - ask questions to whoever is available

Samples- 1. If you separated the girls and boys in the cafeteria and asked 10 from each group about how they felt about the cafeteria food, what kind of sampling is that? a.) Random b.) Systematic c.) Stratified d.) Convenience

2. If you asked the first five people you saw in the hallway about their favorite color, what kind of sampling is that? a.) Random b.) Systematic c.) Stratified d.) Convenience

3. If you asked every third person who walked in the school about how much sleep they got the night before, what kind of sampling is that? a.) Random b.) Systematic c.) Stratified d.) Convenience

** Linear Regression and Correlation ** Sample- What is 4! ? Answer = 24, because 4x3x2x1 = 24. Multiplication rule of counting - How many different types of _ is it possible to create? To find the answer you must multiply all of the options together.Ex: A pizza place offers 3 types of crust, 2 sauces, and 8 different toppings. How many different pizzas can be created by choosing one from each category? Sample- If a store offers shirts in three styles, four colors and three sizes, how many shirts could be chosen? Answer =36 different shirts, because 3x3x4 = 36. Combinations - ORDER DOESN'T MATTER!!!! Any time r objects are randomly chosen from n objects without regards to order=====C n,r=nCr=(__n! )__===== =====(r!(n-r)!)===== On a graphing calculatior under math scroll over to PRBchoose nCr. Permutations- ORDER MATTERS!!!!!!! ** It’s similar to combinations except that order matters. You are still choosing r from a larger set of nearly identical n numbers.Pn,r=nPr= n!/(n-r)!On a graphing calculator go under math, scroll over to PRB then hit nPr ** Elementary Probability ** Intuition is the first method of probability. To assidn an event probability you use previous experiences and knowledge. This type has error because it can differ per person.A second way is to assign probability when outcomes are equally likely. To do this you use this formula:P(event)=number of favorable outcomes/total number outcomesAn example would be finding the probability of pulling a 6 from the deck of cards. You would put 4/52 because there are 4 sixes and 52 cards in a deck. It simplifies to 1/13The last way is relative frequency. You can use the same formula as equally likely. It’s also written asP(event)= frequency of an event/ total number of trials. A example would be A random sample of 500 RLHS students found that 365 need glasses. What is the probability of a student choosen at random needing glasses? The answer would be 73/100 Graphing statistics! __Quartile__ - one of the values of a variable that divides the distribution of the variable into four groups having equal frequencies. __Interquartile range__ __-__ the range of values of a frequency distribution between the first and third quartiles. __Range__ __-__ the extent to which or the limits between which variation is possible. box-and-whisker plot can be useful for handling many data values. They allow people to explore data and to draw informal conclusions when two or more variables are present. It shows only certain statistics rather than all the data. //Five-number summary// is another name for the visual representations of the box-and-whisker plot. The five-number summary consists of the median, the quartiles, and the smallest and greatest values in the distribution. Immediate visuals of a box-and-whisker plot are the center, the spread, and the overall range of distribution. A **pie chart** (or a **circle graph**) is [|circular] [|chart] divided into [|sectors], illustrating percents. In a pie chart, the [|arc length] of each sector (and consequently its [|central angle] and [|area] ), is [|proportional] to the quantity it represents. Stem-and-leaf plots are a method for showing the frequency with which certain classes of values occur. Bar graphs are a very common type of graph best suited for a qualitative independent variable.
 * A correlation is another name for a pattern. The most common type of graph is a line graph. When you graph a paired values data table you are making a scatter plot because the points are scattered all over the graph. Perfect linear correlation is when the scatter plots fall into a straight line. Correlation coefficient is denoted by r. The correlation coefficient lies between -1 and 1. If the correlation coefficient is close to 1 the the correlation has a positive slope. If the correlation coefficient is close to -1 then it has a negative slope. A scatter plot can have no correlation if the slope cannot be deciphered. **============= [[image:factorial.png width="210" height="156"]] Factorial - refers to the multipilcation of an integer with all previous integers down to one and uses the notation; n! A generic formula is n!=(n-1)(n-2)(n-3).... and so onEx: 5! = 5 x 4 x 3 x 2 x 1 = 120To perform this on a calculator hit the math key, scroll over to PRB and it is number 4

A frequency distribuition chart is a tabulation of the values that one or more variables take in a value. Histograms are a bar chart representing a frequency distribution; heights of the bars represent observed frequencies. A pictograph is a graphic character used in picture writing.

Complement of an Event When you add up the probabilities of all outcomes of an occurring event they should equal 1. It is found by P(not A)= 1-P(A) Probability of A and B To find the answer to this you use the formula of P(A and B)=P(A)P(B) With probability of A and B, the events do not affect each other. In this event you find the probability of both situations. Probability of A or B The formula for this is P(A or B)= P(A)+P(B)-PA and B). This is when the events do effect each other. An Example is when you want to find the probability of pulling a king __or__ a queen from a deck. You don’t want to find the probability of both, just one or the other. Odds The odds of the successful outcome of an event is the ratio of the probability of its success to the probability of its failure. The formula is odds =P(success)/ P(failure)


 * Real Life Examples ** (Answers at bottom of page) -

There are many ways that probability can be used in the real world that many people don’t even think about, not to mention it will come up a lot on standardized tests that you need for college. Here are some examples of problems and situations where probability is used in real life situations:

1. There are 11 horses entered in today’s race. You want to know the how many different combinations of first and second there are so you know your odds of winning some money. How can probability help you? à You can use a counting method, permutations, because the order the horses come in matters.

2. Subway is having a special in which you can have a FOUR DOLLAR foot long and you can have any combination of 3 vegetables, 5 types of cheese, 2 types of bread, and 7 types of meat or filling. What is the total number of combinations you could have? à You would use the **multiplication rule of counting** to multiply all the combination options and see how many choices you have.

3. You are at a football game and your friend asks you if you are willing to be $1,937,593,745 that the Red Lion football team is going to beat the steelers that night. You must decide if it is rational to take that bet. How will you decide?!?! à the answer is use intuition which is a type of elementary probability. To do this you use your rationalizing power and life experience to decide the liklihood of something happening.

4. You are taking your SAT’s and come to a 5 choice multiple choice question which you have no idea how to answer. Since you will not be penalized for skipping it, you must find out the probability of guessing and getting it right, so you earn points. How will you decide? à You should use elementary probability and the model for an event.

5. You have a lot of money invested in a black jack game you are playing and you now have to decide whether to chance taking another card or just stay where you are. However, you are at 15 points already. What should you do?? à Use probability to decide what the odds are that your card will keep you at or under 21 points. Assume all the cards have been replaced.

Sampling & Surveys: 1. C, because you are seperating into groups before you are randomly selecting them. 2. D, because it is the first five people, which would be the most convenient. 3. B, because you are using every kth element, which in this case is 3.
 * __//Answers: //__**

1. **Math:** P(11,2) = 11!/ (11-3)! = **990 combinations of first and second.** 2. **Math:** 3 x 5 x 2 x 7 = 210 options 3. **Math:** In this case the math is just logic. Is it rational that a high school team Will beat a professional team? NO! so it is in your best interest NOT to Take the bet. 4. **Math:** P( event) = number of favorable outcomes/ total outcomes 1/ 5 = 20% chance of getting it right. 5. **Math:** needs to be 6 or lower, so options are, Ace, 1, 2, 3, 4, 5, or 6. There are 4 of each in a suit so you have a total of 28 favorable outcomes. 28/52 = about 54% its over half that you will.
 * Real Life Examples: **