SPRINGBOARD UNIT 6 DATA ANALYSIS AND PROBABILITY

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1 SPRINGBOARD UNIT 6 DATA ANALYSIS AND PROBABILITY 6. Theoretical and Experimental Probability Probability = number of ways to get outcome number of possible outcomes Theoretical Probability the probability that should happen Experimental Probability the probability that did happen after an experiment Outcome the result of an experiment Impossible Event an event that cannot occur and has a probability of zero Certain Event an event that will definitely happen and has a probability of one Independent Events when the probability of the first event does not effect the probability of the second event Dependent Events when the probability of the first event does effect the probability of the second event Examples of theoretical probability: Find the probability of randomly choosing January, February, or March out of the 2 months on a calendar as a fraction, decimal, and a percent. =, 0.25, and 25% 2 4 NOTE: Refer back to units and 4 for converting fractions, decimals, and percents. Remember, when changing fractions to decimals, divide the numerator by denominator. Remember, when changing a fraction to a percent, try to get 00 as the denominator. Fred has a bag of marbles. In the bag are blue marbles, 4 red marbles, and yellow marbles. Find the probability of pulling out a blue marble, a red marble, and a yellow marble as a fraction in simplest form. Blue 0 Red 0 4 = 5 2 Yellow 0 Continue.

2 6. Theoretical and Experimental Probability Continued. Example of experimental probability: Jorge rolled a number cube 8 times and rolled the following numbers: 2, 2, 4, 5, 5, 5,, and 6. What is his probability of rolling a, 2,, 4, 5, and 6 as a fraction in simplest form? Rolling a = 8 Rolling a 2= 8 2 = 4 Rolling a = 8 0 =0 Rolling a 4= 8 Rolling a 5= 8 Rolling a 6= 8 Click for live video tutorial: Definitions: events types.html probability Independent Events: events independent.html Dependent Event: event.html

3 6.2 Probability Concepts Jenny found the spinner at the right. She wanted to play a game with some friends but did not know if the game was fair. Find the probability of landing on each section and then determine whether the game is fair. D C A B First divide the spinner into equal parts. There are 8 equal parts. Then find the probability of each section. D C A B P (A)= 8 2 = 4 P(B)= 8 P(C)= 8 2 = 4 P(D)= 8 This is not a fair game because the probability of landing on each section is not the same. There is a greatest chance of landing on D and the smallest chance of landing on B.

4 6. Data Representations Karl took a survey of the 6 th grade students at Sanford Middle School. He asked the students what month they were born in. Below are the results of the survey. Complete the table and create a circle graph and create a bar graph. COMPLETE THE TABLE: Month Number of Students January 0 February 20 March 5 April 0 May 5 June 0 July 5 August 5 September 0 October 0 November 0 December 0 Fraction of Percent of Students Students 0 0 =0 =0% = = 20% = =5% =0 =0% = =5% =0 =0% = =5% = =5% =0 =0% =0 =0% =0 =0% =0 =0% First, find the total number of the students asked. When you add the number of students, there were 00 students surveyed. So all of the fractions have a denominator of 00. Then complete the table. The highlighted yellow columns are the information that was filled in.

5 6. Data Representations Continued CREATE THE CIRCLE GRAPH: Student Birth Months September 0% August 5% November 0% January 0% Be sure to have a title for your graph. Use 5% as benchmarks to create the graph. There are 20 sections that are 5% intervals. First divide the circle graph into 20 equal sections (in yellow). July 5% February 20% Next figure out how many sections each month should have. For example, January is 0% which would be two 5% sections. May 5% April 0% March 5% June, October, and December will not be included in the circle graph because the are 0%. CREATE THE BAR GRAPH: Student Birth Months Number of Students Be sure to have a title for your graph. Be sure to have a vertical and horizontal title for your graph. Create your bars for each category. Month Click for live video tutorial: pie graphs circle graphs Interactive Practice: graph.php

6 6.4 Summarize Data and Make Connections Mean the average. To find mean, add all numbers and divide by the amount of numbers. Median the middle number when numbers are arranged in order from least to greatest. If you have 2 middle numbers, then average them. Mode the number that occurs most often. You can have no mode, one mode, or more than one mode. Range the difference between the largest and smallest numbers. Find the mean, median, mode, and range of the following numbers: 6, 2, 2, 9, 4, 6, 7, 9, First, arrange numbers from least to greatest. 4, 9, 9,, 2, 6, 6, 7, 2 Mean =26. There are 9 numbers, so divide the sum of 26 by =4 Median the middle number is 2. Mode the numbers that occur the most are 9 and 6. Range 2 4=28 Find the mean, median, mode, and range of the dot plot. Pull the numbers out of the plot., 2, 2.5,.5,.5,.5, 4, 4, 4.5, 4.5, 5, 5, 5.5, 5.5, 6.5, 6.5, 7, 8 Mean =82. There are 8 numbers, so divide the sum of 82 by = to the nearest ten the mean is 4.6 Median if there are two middle numbers, then you average them. However, since the two middle numbers are the same, the median is 4.5. Mode the number that occurs most often is.5 Range 8 =7 Click for live video tutorial: the average Measure of Central Tendency: measures.html

7 6.5 Data Collection and Representation When looking at different information on a graph, you always need to look closely to make sure the graphs are not misleading. Below are some examples of misleading graphs. This graph is misleading because the scale does not start at zero. It makes it look like Fresh Squeeze juice has times more juice per serving than Natural Quencher. However, 5% is not times as great as %. This graph is misleading in many ways. First the scale does not start at zero, so it makes it look like there are a lot more people for the pool than against the pool. When the amount of votes is only % different. The bars are also different widths which makes it appear that more people are for the pool. The font used for the bars are also different. The last piece of misleading information is the title. It makes it seem that the community has to have the pool. Click for tutorial: me_examples_of_mislea.htm