Mat 113 1st EditionExam # 2 Study Guide Lectures: 11-18Lecture 11 1. Venn Diagrams a. A survey asked 110 high school athletes which sports they played among football, basketball and baseball. Make a Venn Diagram to represent the following: i. Football only = 24 Athletesii. Basketball only = 13 Athletesiii. Baseball only = 12 Athletesiv. Football, baseball and no basketball = 9 Athletesv. Football, basketball and no baseball = 5 Athletesvi. Basketball, baseball and no football = 10 Athletes vii. All 3 sports = 6 Athletes b. Venn Diagram: i.Lecture 12 1. Percentage Change - You are simply going to find the increase or decrease, divide by the original amount and them multiply by 100 in order to put it into a percent instead of a decimala. Formulai. Percentage Change = Change in function/ Previous function value X 100%2. ExamplesSuppose that there were 35 people in a particular club at the beginning of the semester. At the end of the semester, there were 42 people in the club. What was the percentage change in membership?i. 42-35/35 X 100= 20%(Please note that percentage change will be negative in the case of a decrease). For example, suppose you have $150 in your account at the beginning of October and $79 at the end of October. What is the percentage change in your account during October?II. 79-150/79 X 100 = -47.3%Lecture 131. Scatter Plot Graphs leading to Line Graph A scatterplot is a graph consisting of isolated points, with each dot corresponding to a data point. To make a line graph, we begin with a scatterplot and join the adjacent points with straight-line segments.Example: Once you connect the dots, it makes a line graph and should look like this:2. Bar Graphs a. The bars should not touch in a normal bar graphExample:Lecture 141. Information on graphs Guidelines for creating graphs that meet the requirements for this course: 1. ALWAYS include a detailed title. 2. Label all parts of the graph with clear and appropriate labels, including units whenever proper. 3. Create neat and carefully constructed graphs.* Also note, always be sure to use the appropriate graph for the type of information that you are creating a graph for. Lecture 151. Statistics: The science of conducting studies to collect, organize, summarize, analyze and draw conclusions from dataa. Mean: (Average) of a list of numbers divided by the number of entries in the listb. Median: list of numbers that determines the middle data valuec. Mode: most frequently occurring data points d. Range: highest value minus the lowest value e. Standard deviation: value that describes the spread of data, specifically, how far from the mean the values tend to fall 2. Outlier: data point that is significantly different from most of the dataa. 5 point summary: consists of 5 numbers to summarize data, uses quartiles to divide the datai. 1st quartile: (expressed as Q1), list of numbers where the median is the lower half of the numbers in the listii. 2nd quartile: (expressed as Q2), same as the median of the list iii. 3rd quartile: median of the upper half of numbers in the list iv. also have to find median of entire group of numbers Lecture 161. Bell Curve: Is bell shaped, symmetrical and the mean is equal to the median and is in themiddle 2. Empirical rule: 68%-95%-99.7% rule, between -1 /1 is where 68% of the data lies, between -2 /2 is where 95% of that data lies, between -3/3 is where 99.7% of the data lies Lecture 17Z-score: to find a z-score, you use the formula: Z(x)= X-mean/ Standard deviationExample: Find the % less then 105Z(105)= 105-10 0/10= .5Lecture 181. Margin of error: sample size of a sample (result for the whole population)a. Formula= 100/√n (n= sample size)i. If sample size is 900 (n), you would do 100/ √900, which equals 3.3%2. Sample size= (100/n)23. Correlations a. If both values go up, there is a positive correlationb. If both values go down, there is a negative correlationc. If neither are true, there is no correlation d. If there is a magnitude of 0.8or higher there is a strong correlation. 0.5-0.8 is a moderate correlation and 0.5 and below is a weak