TENNESSEE ADULT EDUCATION 2011 CURRICULUM MATH LEVEL 3 BASIC OPERATIONS CHARTS / GRAPHS, MEAN, MEDIAN, MODE LESSON 3 GRAPHS GRAPHS There are five types of graphs that are typically seen on the GED Bar- show comparisons between data; horizontal Line- compare two variables. Each variable is plotted along an axis Pie- are a type of graph used to represent a part to whole relationship. Scatter- similar to line graphs; map quantitative data points but are not connected with a line

Column show comparisons between data; vertical READING GRAPHS Always read the title of the graph first. Read the title of the vertical and horizontal axis. Read the numbers on the axis and determine what the number represents. Read the categories. If a Key is provided, read the key. ( Usually found on pictographs, line graphs, or multiple bar graphs) What good is a graph if the information is difficult to read? Graphs are read the same way I. Start with the title. All charts/graphs will have a title, usually directly above or below the chart/graph itself. The title tells what the chart/graph is about, think of it as the main idea.

II. The sides of the graph, or the inside parts of a pie graph, are labels that tell what information is being shown. Take time to look at all parts of the graph before answering any of the questions. Key: The graph may or may not have a key. A key is a small area on, or next to, the chart/graph that explains what different shading, colors or patterns featured on the chart/graph stand for or represent. If the graph has a key, read it carefully before reading any of the questions. Bar Graphs Title of graph Vertical Axis Average Rainfall in Inches

25.7 22.02 Honolulu 9.5 7.66 Phoenix 2009 2010 10.5 Dallas 33.7

30.05 New York 47.25 0 5 10 15 20 25 30

35 40 Horizontal Axis 45 50 The scale of a bar graph is always placed on the horizontal axis and information is shown using horizontal (left to right) columns. When constructing bar and column graphs it is often best to start by drawing the horizontal and vertical axis. The next step involves labeling and marking an appropriate scale, including the unit of measurement, on the horizontal (for a bar graph) or vertical (for a column graph) axis.

The remaining axis also needs to be labeled and divisions need to be marked. It is important for every graph to also include a title and a source (where the information is from). Line Graphs 6 5 4 Series 1 Series 2 Series 3 3 2 1 0 Category 1

Category 2 Category 3 Category 4 Line graphs compare two variables. Each variable is plotted along an axis. A line graph has a vertical axis and a horizontal axis. Line graphs have thin lines which often show the trend or change of something or the differences between several things over time. The data on the horizontal axis of a line graph appears from left to right. When constructing a line graph, plot the points first on the graph then connect each point with a single line. Line Graphs have a title and source, and the vertical and horizontal axes (including the units of measurement) should be marked appropriately.

Line graphs are show specific values of data. Line graphs show clear trends in data. Line graphs help to make predictions about where the trends in the data might be going. 1. What was the minimum wage in January, 1978? 2. When did the minimum wage reach $3.35? 3. Between what time periods was the largest increase in minimum wage? 4. Based on your observations of the graph, make a prediction about what the wage might be in the year 2000. 1. What was the minimum wage in January, $2.65 1978?

2. When did the minimum wage reach $3.35? 1981 3. Between what time periods was the largest increase in minimum wage? 1996-1997 up $.40 4. Based on your observations of the graph, make a prediction about what the wage might continue to increase be in the year 2000. PIE GRAPH Basic Math add 2 decimal 1

subt 1 7 addition mult divide 4 subtraction 1 4

2 7 multiplication fraction decimal percent time place value Circle graphs, also called pie charts or pie graphs, are a type of graph used to represent a part to whole relationship. Properties of Circle Graphs: Circular shaped graphs with the entire circle representing the whole. The circle is then split into parts, or sectors.

Each sector represents a part of the whole. Each sector is proportional in size to the amount each sector represents, therefore it is easy to make generalizations and comparisons. Graph Title--A graph title gives an overview of the information displayed in the graph. The title is given at the top of the graph. Sectors--Each sector represents one part of the whole. The size of each sector represents its fraction of the whole. Sector Labels--The label of each sector indicates the category of information in which it refers. Reflects numeric data (often a percentage) so we know the size of each sector. Title Statewide enrollment for GED

KEY 6.20% 12.20% 32.40% What information does the title tell you about this pie graph? Statewide enrollment 49.20% Literacy Basic Skills Pre-GED

GED What percent of students are enrolled Pre-GED? 33% What percent of students are in GED classes? 12% Approx. what fraction of students are enrolled in basic skills? 1/2

TITLE Basic Math KEY add 2 decimal 1 subt 1 7

addition mult divide 4 subtraction 1 4 2 7 multiplication fraction

decimal percent time place value The pie / circle graph above has a large key section. In this case, every different color stands for a different math skill. Using different colors makes the graph much easier to read, and the reader can immediately see which sections are large or small. SCATTER GRAPH Y-Values 3.5 3 2.5 2 Y-Values

1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 Scatter graphs are similar to line graphs.

Scatter graphs map data points. Each point represents specific data. With a scatter plot graph, individual points are not connected directly together with a line but, instead express a trend with the dots. To see the trend the data points will be clustered together. Scatter plot graphs are a statistical tool used to mathematically express a trend in the data. With a scatter plot graph, a dot or small circle represents a single data point. With one mark (point) for every data point, visual data can be seen. Depending on how tightly the points cluster together, you may be able to understanding a clear trend in the data. COLUMN GRAPH Skill Breakdown by OPT

60 50 40 Percent 30 20 10 0 graph/charts/tables basic math algebra/geometry PB PC PD PE

OPT PF PG A column graph has numerical values that are illustrated with horizontal columns. Column graphs are particularly effective for showing values that are categorized by two separate characteristics, such as year and sector. Skill Breakdown by OPT 60 50 40 Pe rcent 30

20 10 0 graph/charts/tables basic math algebra/geometry PB PC PD PE PF PG

OPT Using the graph above, what is main idea? skill breakdown by opt (title) What are the labels of this graph? Graph/charts/tables, basic math, algebra/geometry (key) What test has the highest percent of basic math questions? PG What test has the highest percent of subject/verb agreement questions? No information about subject / verb agreement In what tests are the percentages of basic math and algebra/ geometry the same?

PF and PB PB OPT Skill Breakdown Percentage 40 36 32 30 20 20 percentage 12 10 0

graphs basic math algebra geometry Answer the questions using the above graph 1.What percent of the PB Official Practice Test questions concern graphs? 2. What percent of the PB Official Practice Test questions concern geometry? 3. What percent of the PB Official Practice Test questions concern basic math?

4. What percent of the PB Official Practice Test questions concern algebra? 36% 20% 32% 12% MEAN, MEDIAN, & MODE Before you can begin to understand statistics, there are three terms seen on the GED test. Mean, Median, Mode Mean: another word for average Median: the middle number in a list of numbers Mode: the number used most often

MEAN: AVERAGE Average is a familiar term. Used in grade school when looking at report cards. Add together all of the test results and divide it by the sum of the total number of marks (grades) there are. The average is also known statistically as the Mean! If daily quizzes for math class are tracked and the results are: 75, 18, 90, 50, 100, 100 The sum of the quizzes equals 433 Divide 433 by 6 / number of quizzes

The 'Mean' (Average) is 72.17 MEAN Add up all given numbers : 4,12,4,20 4 + 4 + 12 + 20 = 40 Since there are 4 numbers divide the total 40 by 4 Mean or Average to the given set of numbers: 10 MEDIAN The Median is the 'middle value' in the list of given numbers.

When the totals of the list are odd, the median is the middle number. Sort the list of numbers from smallest to largest. 12,15,17,9, 32 9,12,15,17,32 Median is 15 When the totals of the list are even, the median is equal to the sum of the two middle numbers divided by 2. Sort the list of numbers from smallest to largest. Take the two middle numbers, add together and divide by two. List the numbers, the middle number is the median! Be sure to remember the odd and even rule. GUIDED PRACTICE Find the Median: 7, 64, 24, 19, 17,12,59 (odd amount of numbers)

Line up your numbers: 7,12, 17, 19, 24, 59, 64 (smallest to largest) The Median is 19 (The number in the middle) Find the Median of: 18, 31, 44, 26, 12, 16 (Even amount of numbers) Line up your numbers: 12, 16, 18, 26, 31, 44 Add the 2 middles numbers and divide by 2: 18 + 26 = 44 2 The Median is 22 MODE The mode in a list of numbers refers to the list of numbers that occur most frequently. A trick to remember this one is to remember that mode

starts with the same first two letters that most does. Most frequent - Mode. You'll never forget that one! Find the mode: 19, 17, 13, 44, 17 , 17, 44, 15, 25, 15, 27, 41, 17, Put the numbers in order from least to greatest: 13, 15,15, 17, 17, 17 ,17,19, 25, 41, 44 Mode is 17 GUIDED PRACTICE Find the mode: 29, 25, 10, 44, 25 , 25, 44, 15, 33, 15, 27, 41, 25,15 Arrange numbers from smallest to largest: 10, 15, 15, 15, 25, 25, 25, 25, 27, 29, 33, 41, 44, 44 The Mode is

25 Find the mode: 9, 10, 14, 13, 13, 9, 16, 9 Arrange numbers: 9, 9, 9, 10, 13, 13, 14, 16 The Mode is 9 REVIEW: MEAN, MEDIAN, MODE Mean = is another word for average Add up all given numbers 4 + 4 + 12 + 20 = 40 Since there are 4 numbers divide the total 40 by 4 Answer is 10

Median = is the middle number in a list of numbers Ex: 2, 4, 6, 7 , 9, 12, 15 Be sure to remember the odd and even rule. Mode = is the number used most often Ex: 12, 12, 10, 14, 13, 13, 12, 16 Another way to remember median is traveling the interstate- Lanes travel east and west and the middle section is called the median.