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Since there are ten marbles total possible outcomes and three green marbles favorable outcomes , the probability is 3 out of 10 or 3. Statistics The study of numerical data and its distribution is called statistics. The three basic measures indicating the center of a distribution are: mean, median, and mode. Mean, Arithmetic Mean, or Average To find the average of a group of numbers: 1. Add them up. Divide by the number of items you added.

What is the average of 10, 20, 35, 40, and 45? What is the average of 0, 12, 18, 20, 31, and 45? What is the average of 25, 27, 27, and 27?

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Median A median is simply the middle number in a list of numbers that have been written in numerical order. For example, in the following list3, 4, 6, 9, 21, 24, 56the number 9 is the median. If the list contains an even number of items, average the two middle numbers to get the median.

For example, in the following list5, 6, 7, 8, 9, 10the median is 7 1. Because there is an even number of items, the 2 average of the middle two, 7 and 8, gives the median. The list has to be in numerical order or put in numerical order first. The median is easy to calculate and is not influenced by extreme measures. Mode A mode is simply the number most frequently listed in a group of numbers. For example, in the following group5, 9, 7, 3, 9, 4, 6, 9, 7, 9, 2the mode is 9 because it appears more often than any other number.

There can be more than one mode. If there are two modes, the group is called bimodal. Data Analysis: Graphs Information can be displayed in many ways.

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The three basic types of graphs you should know about are bar graphs, line graphs, and circle graphs or pie charts. You should also know the scatter plot, which is similar to a coordinate graph. When answering questions related to a graph:.

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Examine the entire graphnotice labels and headings. Focus on the information given. Look for major changeshigh points, low points, trends. Do not memorize the graph; refer to it. Pay special attention to which part of the graph the question is referring to. Reread the headings and labels if you dont understand.

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Bar Graphs Bar graphs convert the information in a chart into separate bars or columns. Some graphs list numbers along one edge and places, dates, people, or things individual categories along the other edge. Always try to determine the relationship between the columns in a graph or chart. The following bar graph indicates that City W has approximately how many more billboards than City Y?

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The graph shows the number of billboards in each city, with the numbers given along the bottom of the graph in increases of The names are listed along the left side. City W has approximately billboards. The bar graph for City Y stops about halfway between and Consider that halfway between and is So City W has approximately more billboards than City Y Based on the following bar graph, answer these questions: A.

The number of books sold by Mystery Mystery from to exceeded the number of those sold by All Sports by approximately how many? From to , the percent increase in number of books sold by All Sports exceeded the percent increase in number of books sold by Mystery Mystery by approximately how much? What caused the decline in Reference Unlimiteds number of books sold?

The graph contains multiple bars representing each publisher.

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Each single bar stands for the number of books sold in a single year. You might be tempted to write out the numbers as you do your arithmetic 3. Writing out the numbers is unnecessary, as it often is with graphs that use large numbers. Since all measurements are in millions, adding zeros does not add precision to the numbers. Totaling the number of books sold for all three years gives 8. Again, use a piece of paper as a straightedge, but dont designate numbers beyond the nearest 10th because the graph numbers prescribe no greater accuracy than this.

Totaling the number of books sold for all three years gives 6. So, the number of books sold by Mystery Mystery exceeded the number of books sold by All Sports by 2. Answer to Question B. The formula for figuring either of these is the same. Never assume information that is not given. In this case, the multiple factors that could cause a decline in the number of books sold are not represented by the graph. Line Graphs Line graphs convert data into points on a grid.

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These points are then connected to show a relationship among items, dates, times, and so on. Notice the slopes of the lines connecting the points. These lines show increases and decreases the sharper the slope upward, the greater the increase; the sharper the slope downward, the greater the decrease. Line graphs can show trends, or changes, in data over a period of time.

Based on the following line graph, answer these questions: A. In which year period was there the greatest decrease in the property value of Moose Lake Resort? Answer to Question A. The bottom of the graph shows the years from to According to the following line graph, the tomato plant grew the most between which two weeks? The numbers at the bottom of the graph give the weeks of growth of the plant.

The numbers on the left give the height of the plant in centimeters. The sharpest upward slope occurs between week 3 and week 4, when the plant grew from 40 centimeters to 80 centimeters, a total of 40 centimeters growth. Based on the following circle graph: Smithville Community Theater Expenditures. What is the ratio of the amount of money spent on advertising to the amount of money spent on set construction? Based on the following circle graph:. The amount of money spent on field trips in was approximately what percent of the total amount spent?

Scatter Plot A scatter plot is a graph representing a set of data and showing a relationship or connection between the two quantities given. The graph is typically placed in one part of a coordinate plane the upper right quarter called Quadrant I. When the data is placed on the scatter plot, usually a relationship can be seen.

If the points appear to form a line, a linear relationship is suggested. If the line goes up to the right, that is, one quantity increases as another increases, then the relationship is called a positive correlation. For example: Biology test score out of possible 90 80 70 60 50 1 2 3 4 5 6 7. If the line goes down to the right, that is, one quantity decreases as another increases, then the relationship is called a negative correlation. For example: Grade point average. If the data does not appear to show any line or any relationship between the quantities, the scatter plot is said to show no correlation.

Note: Remember that multiple-choice problems range from easy to average to difficult. Number and Operations Operations with Fractions 1. If 2 of 2 ' 5 is divided by 3 , what is the 3 6 10 5 resulting value?

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The weight of coffee in a bag is 3 pound. A coffee 4 company packages 12 of these packages in a case. If the coffee company fills an order for 4 1 cases 2 how many pounds of coffee will the company need to fill this order? Explanations 1. To get rid of all the fractions in the second step, multiply the 2.

Multiply 3 by The product is 9, which is the weight of coffee in one case. Next, multiply 9 4 2 by 4 1. The correct answer is 81 or How much profit, per DVD, does the owner make during the special sale?