Unit 9: Probability, Statistics and Percents Section 1: Relative Frequency and Probability The frequency of something is how often it happens Relative frequency is based on an actual experiment that has been conducted Relative frequency can be given as a decimal, a fraction, or a percent (all are acceptable unless you are specifically asked to give it a certain way) To find the relative frequency of an event: # of times an event occurred # of times the event could have occurred

Ex1. What is the relative frequency of boys in this class? Probability is much like relative frequency, but it is based on what might happen (there has been NO experiment run) Ex2. A regular six-sided die is rolled, what is the probability that the number is greater than 2? The probability of an event is written P(E) Remember that in Unit 1, the number of elements in a set was written N(X) In order to determine probability, it is essential that all outcomes are equally likely

Two events are complements if they have no elements in common and together they make up every possibility The probabilities of complementary events have a sum of 1, so if you know the probability of one of them, you can determine the other Ex3. If the probability of rain tomorrow is 30%, what is the probability that it doesn’t rain? Open your book to page 373 (green table) Section of the book to read: 6-4

Section 2: Probability in Geometric Regions Area of a circle: A = πr² To find the probability of a geometric region, the numerator will be the area of the desired section and the denominator will be the entire area possible When dealing with circles, use the pi symbol on your calculator (not an approximation) Do not round until the VERY last step (use the ANS function on your calculator)

Ex1. Suppose a dart thrown lands in the rectangle. What is the probability that it lands within the circle? 30 meters 50 meters 110 meters

Ex2. What is the probability a dart would hit the shaded region, assuming it hits somewhere on the target? 8 m 12 m 20 m

Ex3. What is the probability that the spinner lands on the number 3? Section of the book to read: 6-6

Section 3: Measures of Central Tendency and Measures of Spread The measures of central tendency are mean, median and mode (they measure the approximate “center” of the data) To find the mean: add up all of the numbers and divide by how many terms there are To find the median: put all of the numbers in order from least to greatest and the median is the number in the middle (if there are 2 central numbers, find the mean of the two)

To find the mode: name the number(s) that occur most often (there may be no mode, one mode, or multiple modes) A frequency table is a table in which all of the terms of a data set are put into a table that demonstrates the frequency of each term The measures of spread are: range, standard deviation and variance The measures of spread measure how much the terms of the data set are spread out To find the range: maximum – minimum

To find the variance (s²): 1) Find the mean 2) Find each term minus the mean 3) Square each of the answers from step 2 4) Add each of the answers from step 3 5) Divide the answer from step 4 by one less than the total number of data points To find the standard deviation (s): take the square root of the variance

Ex1. 25, 32, 38, 21, 23, 32, 52, 19, 38, 46 a)Find the mean b)Find the median c)Find the mode d)Find the range e)Find the variance f)Find the standard deviation

Section 4: Scatter Plots and Lines of Best Fit Scatter plots are graphs of unconnected points representing data If the points come close to falling in a linear pattern the are said to have a strong correlation The closer the points are to being linear, the stronger the correlation If the points appear to have a positive slope, then the correlation is positive (the same is true with negative)

Ex1. Describe the likely correlation between the variables studied in each case as positive, negative, or little to none. a) age and height (birth to age 20) b) shoe size and income To find a line that comes close to describing the linear relationship (from Unit 4 Section 7): a) Draw a line through the “center” of the data b) Find the coordinates of 2 points on the line c) Use those two points to find the equation of the line

Graphing calculators can find the line of best fit, or the best possible line through data points – we will practice this now Ex2. (5, 6), (8, 12), (4, 1), (-2, -7), (1, 0), (-6, -4), (-1, -3), (6, 3), (5, 9), (8, 7) a) Graph the points on a scatter plot b) Draw a linear regression model b) Find the line of best fit Section of the book to read: 3-3

Section 5: Visual Displays of Data To make a circle graph: a) find the total number of data points b) divide the desired outcome by the total number of data points and multiply by 360° (this is the number of degrees for that section) To make a bar graph: a) Determine the frequency of each outcome b) Draw a quadrant I graph with the frequency on the y-axis and the outcome on the x-axis c) Draw each bar accordingly

To make a box plot: 1) Put all of the numbers in order from least to greatest 2) Find the median. This is the second quartile Q 2 3) Find the median of the remaining numbers below the 2 nd quartile. This is the 1 st quartile Q 1 4) Find the median of the remaining numbers above the 2 nd quartile. This is the 3 rd quartile Q 3 5) Find the maximum and the minimum 6) Draw in the appropriate format

Use a proportion to find the number of degrees for each section Use a different proportion to find the percentage Give a title to the graph Circle Graph

Remember to title the graph and label the axes Notice that the bars do NOT touch Make the bars reasonably wide Bar Graph

End lines are often dots instead Graph is still titled Box Plot (a.k.a. Box and Whisker Plot)

Ex1. Make a circle graph of the following information. You interview 50 people. 16 say their favorite color is green, 12 say blue, 19 say red and 3 say purple. Ex2. Make a bar graph of the same information from Example 1. Ex3. Make a box plot of the following data. 3, 4, 2, 6, 4, 6, 13, 14, 7, 8, 8, 3, 15, 9, 10, 11, 4, 12, 16, 20

Section 6: Percents In Equations To set up an equation involving percents, plug information into % · of = is The percent must be in decimal form Another way to think of that equation is % · whole = part Set up an equation and solve. Ex1. What is 123% of 80? Ex is what percent of 1800? Ex3. 12 is 86% of what number?

Ex4. In 1992, there were 207,828 women serving in the Armed Forces of the US, accounting for 11.5% of total military personnel. In all, how many people were serving in the Armed Forces in 1992? Write an equation and solve. The other way to solve percent questions is with a proportion or With proportions, the percent is NOT in decimal form Section of the book to read: 6-5