4.  Mean: Average  Median: Middle of an ordered list  Exact middle for an odd # of items  Average of the middle two for an even # of items  Mode: Most frequent  Range: Highest - Lowest

5.  Helps you to see where the majority of the data lies, as each part is 25% of the data  Lowest and highest values = endpoints  Median of the data = center of the box  Median of the lower part and upper part = edges of the box

6. low Q1 median Q3 high lowest 25% 2 nd 25% 3 rd 25% highest 25% the box contains 50% of the data Outliers are 1.5. IQR from the ends of the box  IQR = Q3 – Q2 Extreme Outliers are 3∙IQR from the ends of the box The high and the low are not always Outliers, not all data sets contain outliers.

7.  Relatively evenly distributed (normal) data  Skewed left (longer left tail)  Skewed right (longer right tail)  Skew is determined by the tail

8. Draw boxplot for the following test scores: 98, 75, 80, 74, 92, 88, 83, 60, 72, 99 Try before checking the answer below Ordered list: 60, 72, 74, 75, 80, 83, 88,92, 98, 99 Draw a number line Plot the end points Find the median Find the median of the first half Find the median of the second half Draw the box around the “three” medians Connect the box with “whiskers” to the endpoints 60 70 80 90 100

9.  Displays all data  Stem Leaf 1 st #(s) Last #

10.  Similar to a stem and leaf plot but does not necessarily retain the precise values of the data  Given: 10, 18, 21, 26, 30, 31, 38, 40  Create both a stem and leaf and a dotplot then check your answer below  Stem and LeafDot Plot 1 0, 8 2 1, 6 3 0, 1, 81 2 3 4 4 0

11. 10 2 5 7 20 1 6 30 5 8 9 9 40 2 3 5 7 8 50 2 60 3 6 the median the middle of the 17 values or 309 the first quartile the middle of the first half or (201+206)/2=203.5 the third quartile the middle of the second half or (407+408)/2=407.5 the inter-quartile range the difference of the quarter points 407.5-203.5=204 the mode the most frequent 309 the percentile for 305 305 if the 5 th item, 5/17=.294 * 100= 29.4 or the 29 th percentile the value closest to the 60 th percentile 60/100=x/17.6 = x/17.6*17 = x 10.2 = x the 10 th item (402) is closest to the 60 th Percentile Find the standard deviation enter all the data in L1 press STAT  calc, choose one-var stat St. dev. = Ϭ x EXAMPLE: Given the following stem and leaf plot FIND each of the requested items then check your answers to the right

12.  Shows how many and approximate values of the data  If the points follow a pattern, you can find the regression line

13.  Use the following data for the next several slides:  (1, 5), (2, 11), (3, 16), (4, 20)  Press 2 nd + 7 1 2 (clears everything) ◦ Press 2 nd + 5 1 2 for a regular TI-83  Press 2 nd 0 x -1 find diagnostics on press enter  Press Stat enter  X’s go in L1  Y’s go in L2  Press Y=, arrow up to plot 1press enter, zoom 9

14.  Decide what pattern the points appear to be following  Press STAT arrow over to calc  Choose the correct pattern  4 for linear  5 for quadratic  0 for exponential  Press variable, arrow to y-vars, press 1, press 1, enter  Write down the value of r  Press Y= write down the equation to 3 decimal places  Press graph to see the fit

15.  Predicting knowing x try using x = 3.5  Set the window to be large enough for the given value  Graph  Press 2 nd trace (calc)  Choose 1 (value)  Enter the value and press enter  Estimating knowing y try using y =18  Set the window to be large enough for the given value  Enter the value in Y2=  Press 2 nd trace (calc)  Choose 5 (intersect)  Press enter three times  You may also substitute values into the equation

16.  Find the equation for the following data and determine the value when x = 2 and when x = 7 xy -5 0-2 10 31 43 54 66 Scatterplot—enter data in stat edit Linear regression values Graph to make sure the line fits the pattern Use the calculations and enter a value of 2 Use the calculations and enter a value of 7 Click on the calculator to see a video on how to find a regression line if you did not get the correct values Now try it for your self, checking along the way to see if you have the same values/screen shots as below—click each time you are ready to check your calculations.

18. How can we determine all the possible outcomes of a given situation? TREE DIAGRAM—an illustrative method of counting all possible outcomes. List all the choices for the 1 st event Then branch off and list all the choices for the second event for each 1 st event, etc.

19.  Try the following then check below  A restaurant offers a salad for $3.75. You have a choice of lettuce or spinach. You may choose one topping, mushrooms, beans or cheese. You may select either ranch or Italian dressing. How many days could you eat at the restaurant before you repeat the salad? Lettuce spinach mushrooms beans cheese mushrooms beans cheese ranch Italian ranch Italian ranch Italian ranch Italian ranch Italian ranch Italian

20. While the tree diagram is beneficial in that it lists every possible outcome, the more options you have the more difficult it is to draw the diagram. Fundamental counting Principle—is a mathematical version of the tree diagram, it gives the # of possible ways something can be accomplished but not a list of each way.

21.  Example: try before checking your answer Jani can choose from gray or blue jeans, a navy, white, green or stripped shirt and running shoes, boots or loafers? How many outfits can she wear? _______ ______ _______ pants shirts shoes 243=24

22. Permutations—all the possible ways a group of objects can be arranged or ordered (the way things are listed matters) Example: There are four different books to be placed in order on a shelf. A history book (H), a math book (M), a science book (S), and an English book (E). How many ways can they be arranged? 24 WAYS 4 3 2 1 = 24 H, M, S, E H, M, E, S H, S, E, M H, S, M, E H, E, M, S H, E, S, M M, E, S, H M, E, H, S M, S, H, E M, S, E, H M, H, E, S M, H, S, E S, M, E, H S, M, H, E S, H, M, E S, H, E, M S, E, M, H S, E, H, M E, M, S, H E, M, H, S E, H, M, S E, H, S, M E, S, M, H E, S, H, M

23. A permutation of n objects r at a time follows the formula This can be done on your calculator with the following keystrokes: Type the number before the P Press math  Over to prb Choose number 2 nPr Enter the number after the P Press enter. Now Try 8 P 3

24. Combinations—the number of groups that can be selected from a set of objects --the order in which the items in the group are selected does not matter How can you determine the difference between a permutation and a combination?

25. Example: How many three person committees can be formed from a group of 4 people—Joe, Jim, Jane, and Jill Joe, Jim, Jill Joe, Jill, Jane Joe, Jim Jane Is Joe, Jane, Jim A different committee Jim, Jane, Jill Formula: Using the same basic steps on the calculator but choosing n C r find 8 C 3 Is there a difference in value for 8 C 3 and 8 P 3 For the problem above:

26. This can be done on your calculator with the following keystrokes: Type the number before the C Press math  Over to prb Choose number 3 n C r Enter the number after the C Press enter. Using the same basic steps on the calculator but choosing n C r find 8 C 3 Is there a difference in value for 8 C 3 and 8 P 3

27.  What is the difference between replacement and repetition?

28. Replacement—being allowed to use the same object again (n r ) Example: try each before checking The keypad on a safe has the digits 1- 6 on it how many: a) four digit codes can be formed _____ _____ b) four digit codes can be formed if no 2 digits can be the same _____ _____ 6666 6543

29. Repetition —occurs when you have identical items in a group Example: Find all arrangements for the letters in the word TOOL ____ ____ TOOLOLOTLOTO TOLOOLTOLOOT TLOOOTOLLTOO OTLO OOTL OOLT We would expect 24 but since you can’t distinguish between the two O’s all possibilities with the O’s switched are removed we divide by the number of individual repetitions—that is 24/2 = 12 which is what we have 4321

30. Formula for repetitions: where s and t represent the number of times different items are repeated EXAMPLE: try then check How many ways can you arrange the letters in BANANAS A’s N’s The factorial key is also found by pressing math and arrowing over to PRB

31. ?2 1 3 4 Circular Permutation—arranging items in a circle when no reference is made to a fixed/starting point Example: How many ways can you arrange the numbers 1-4 on a spinner? We would expect 4! Or 24 ways but we only have 6 Circular permutations are always (n-1)! A1 2 3 4 B1 2 4 3 C1 3 2 4 D1 3 4 2 E1 4 2 3 B1 4 3 2 ?2 1 3 4 D

32.  How many ways can 6 charms be arranged on a bracelet that does not have a clasp.  (6-1)! = 5! = 120 ways

33. If all outcomes are successful, the probability will be 1 If no outcomes are successful, the probability will be 0 So Probability is 0 ≤ P ≤ 1

34. Try the following examples then check below: What is the probability of getting an ace from a deck of 52 cards? 4 aces so What is the probability of rolling a 3 on a 6 sided die? there is one 3 on 6 sides so

35. Try each then check: What is the probability of rolling an even number? 2,4, 6 are even so What is the probability of getting 2 spades when 2 cards are dealt at the same time? at the same time indicates the use of a combination —hint there are 13 spades

36. What is the probability of getting a total of 5 when a pair of dice is rolled? +123456 1234567 2345678 3456789 45678910 56789 11 6789101112 Draw the following chart for the sum of all rolls and count how many have a sum of 5

37. OR: P(A or B) = P(A) + P(B) – P(A and B) Example: What is the probability of getting a 2 or a 5 on the roll of a die? Exclusive Events: events that do not have bearing on each other  What is meant by compound probability?  The words or & and are in the problem

38. Try then check What is the probability of drawing an ace or a heart? ace + heart – ace of hearts + - = Events are inclusive if they have overlap!

39. AND: indicates multiplication Examples: try then check What is the probability of tossing a three of the roll of a die and getting a head when you toss a coin? three and a head * = These events are independent—have no effect on the outcome of the other