Eddie Keel

Algebra I EOC Cheat Sheet: Standard 5 I.

Theoretical Probability a. Definition: Probability is a likelihood that an event will happen. b. We can find the theoretical probability of an event using the following ratio:

c. Example: If we toss a fair coin, what is the probability that a tail will show up? i. Solution: Tossing a tail is the favorable outcome here. When you toss a coin there are only 2 possible outcomes: a Head or a Tail. So the options for tossing a tail are 1 out of 2. We can also represent probability as a decimal or as a percent. d. Example: A bag contains 20 marbles. 15 of them are red and 5 of them are blue in color. Find the probability of picking a red marble. i. Solution:

e. Example: Find the probability of getting a sum of 7 when you roll two dice. i. Solution: There are six numbers on a die: 1, 2, 3, 4, 5, and 6. There are 6*6=36 possible outcomes. You can roll a sum of 7 in the following manner: (1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1). So, there are six (6) ways to roll a sum of 7 when you roll two dice. So, the probability of getting a sum of 7 when we roll two dice is:

II.

III.

Complement of an Event a. Definition: The Complement of an Event is all the other possible outcomes of the respective experiment. b. If A is an event of an experiment, then its complement is denoted by Ac. c. Example: What is the probability of rolling a 2 on a fair six-sided die? i. Answer: 1/6 d. Example: What is the probability of NOT rolling a 2 on a fair six-sided die? i. Answer: 1 – 1/6 = 5/6 since there are 5 numbers on a die that are not a 2! e. Example: Ethan has 70% chance of winning the car race. What is the probability of Ethan not winning the race? i. Solution: P(not winning) = 100% - 70% = 30% Relative Frequency a. Example: Joe spun the spinner and recorded the results in the table as shown. What is the experimental probability of spinning a 2? Number of times. i. Solution: Joe spun the spinner 30 Outcomes spins of 8 times. He spun the number 2 a total P(spin 2) = 8/30 = 4/15. 1 2 b. Example: Using the same table, what is the 2 8 experimental probability of NOT rolling a 2? 3 8 i. Solution: P(not spinning 2) = 22/30 = 11/15

4

12

Algebra I EOC Cheat Sheet: Standard 5 IV.

Line of Best Fit

1. Enter the data in the calculator lists. Place the data in L1 and L2. STAT, #1Edit, type values into the lists

2. Prepare a scatter plot of the data. Set up for the scatterplot. 2nd StatPlot - choices shown at right. Choose ZOOM #9 ZoomStat. Graph shown below.

Eddie Keel

Algebra I EOC Cheat Sheet: Standard 5

Eddie Keel

3. Have the calculator determine the line of best fit. STAT → CALC #4 LinReg(ax+b) Include the parameters L1, L2, Y1.

(Y1 comes from VARS → YVARS, #Function, Y1)

You now have the values of a and b needed to write the equation of the line of best fit. See values at the right. y = 11.73128088x + 193.8521475

4. Graph the line of best fit. Simply hit GRAPH. To get a predicted value within the window, hit TRACE, up arrow, and type the desired value.

Question: Predict the total calories based upon 22 grams of fat. ANS: 451.940 calories

V.

Quartiles a.

Quartiles can be thought of as percentile measure. Remember that quartiles break the data set into 4 equal parts. If 100% is broken into four equal parts, we have subdivisions at 25%, 50%, and 75% creating the: th i. Q1: First quartile (lower quartile) to be at the 25 percentile. th ii. Median (or second quartile) to be at the 50 percentile. th iii. Q3: Third quartile (upper quartile) to be a the 75 percentile.

Algebra I EOC Cheat Sheet: Standard 5 VI.

Correlation

Eddie Keel

Algebra I EOC Cheat Sheet: Standard 5 VII.

Eddie Keel

Box-and-Whisker Plots

We know that the median of a set of data separates the data into two equal parts. Data can be further separated into quartiles. Quartiles separate the original set of data into four equal parts. Each of these parts contains one-fourth of the data. b. Quartiles are percentiles that divide the data into fourths i. The first quartile is the middle (the median) of the lower half of the data. One-fourth of the data lies below the first quartile and three-fourths lies above. (the 25th percentile) ii. The second quartile is another name for the median of the entire set of data. Median of data set = second quartile of data set. (the 50th percentile) iii. The third quartile is the middle (the median) of the upper half of the data. Three-fourths of the data lies below the third quartile and one-fourth lies above. (the 75th percentile) c. A quartile is a number, it is not a range of values. A value can be described as "above" or "below" the first quartile, but a value is never "in" the first quartile. a.

d.

Consider:

Check out this five statistical summary for a set of tests

scores.

e. While we do not know every test score, we do know that half of the

scores is below 80 and half is above 80. We also know that half of the scores is between 70 and 90. The difference between the third and first quartiles is called the interquartile range, IQR. (For this example, the interquartile range is 20.) f. The interquartile range (IQR), also called the midspread or middle fifty, is the range between the third and first quartiles and is considered a more stable statistic than the total range. The IQR contains 50% of the data.

Algebra I EOC Cheat Sheet: Standard 5 g.

Eddie Keel

A five statistical summary can be represented graphically as a box and whisker plot. The first and third quartiles are at the ends of the box, the median is indicated with a vertical line in the interior of the box, and the maximum and minimum are at the ends of the whiskers.

h. Box-and-whiskers on a TI-83

Algebra I EOC Cheat Sheet: Standard 5

Eddie Keel

Algebra I EOC Cheat Sheet: Standard 5 VIII.

Measures of Central Tendency

Eddie Keel

Algebra I EOC Cheat Sheet: Standard 5

IX.

Mean and Median on a TI-83

Eddie Keel

Algebra I EOC Cheat Sheet: Standard 5

Eddie Keel