Elementary Review over GRAPHS!!! Seriously…students seem to forget this stuff. Outcome 5, Component 2

Pictograph Types of Graphs Line Graphs Plots Circle Graph Histogram Single Double Stem & Leaf Line Single Double Box - and - Whisker Plot Scatter Bar Graphs

Pictograph More Info Fireflies Days of the Week

Pictograph b All pictographs have a title. b Rows and columns shape the pictograph. b Label each row and column. b Use pictures to show the data. b Each picture equals a certain amount of data. b Pictographs need a key. Return to Graph

Bar Graph More Info

Bar Graph b The purpose of a bar graph is to display and compare data. b Bar graphs use bars to show the data. b A bar graph must include: - a title - a title - labeled X and Y axes - labeled X and Y axes - equal intervals are used on the Y axis - the bars are evenly spaced apart from each other Return to Graph

Double Bar Graph More Info

Double Bar Graph b The purpose of a double bar graph is to compare two or more sets of data. b Uses bars to show the data. b Double bar graphs must include: - Title - Title - Labeled X and Y axes - Labeled X and Y axes - Equal intervals are used on the Y axis - Pairs of bars are equally spaced, but the compared bars are not - Key Return to Graph

Histogram Frequency Test Scores Class Test Scores More Info

Histogram b Histograms are used to show the frequency of data. b Very similar to bar graphs, but use intervals on the X axis. b Bars do touch. b Histograms have a title. b Histograms have two axes which are labeled. Return to Graph

Line Graph More Info

Line Graph b A line graph is used to illustrate change over time. b Line graphs need: - Title - Title - Labeled X and Y axes - Labeled X and Y axes - Equal Intervals - Equal Intervals - Data displayed by points connected into lines Return to Graph

Double Line Graph More Info

Double Line Graph b A double line graph is used to compare two groups of related data over time. b Double line graphs need: - Title - Title - Labeled X and Y axes - Labeled X and Y axes - Equal Intervals - Data displayed by points connected into lines - Key Return to Graph

Circle Graph More Info

Circle Graph b Circle graphs are used to display parts of the data in relation to the entire amount of data. b All circle graphs need a title. b Each part is called a sector and is labeled. b All angles correct (+2/-2 degrees) Return to Graph

Line Plot Favorite Colors X XXX XXXX XXXXX RedBlueGreenYellowPurple More Info

Line Plot b A line plot shows the spread of all the data on a number line. b Easily identifies the mode. b All line plots include: - a title - a title - a numbered horizontal line - a numbered horizontal line - data displayed by use of X’s - data displayed by use of X’s Return to Graph

Stem and Leaf Plot Student Heights in Centimeters Key: 127 = 127 cm More Info

Stem and Leaf Plot b Stem and leaf plots are used as a quick way of seeing how many pieces of data fall in various ranges. The reader can quickly tell: - the range - the range - the mode - the mode b Stem and leaf plots have a title, a stem, and leaves b A key is used to explain how to read the stem and leaves. Return to Graph

Scatter Plot Study Time Versus Grades Study Time in Hours Grade * * * * * * * 5 More Info

Scatter Plot b Shows how closely two sets of data are related b The closer the sets are related, the closer the points come to forming a straight line. b Scatter Plots include: - title - labeled axes - equal intervals - corresponding numbers plotted as ordered pairs Return to Graph

Box - and - Whisker Plot Hours of Homework More Info

Box - and - Whisker Plot b Displays large set of data. b Gives general idea of how data clusters. b Graph includes: - Title - Title - Labeled intervals - Box between lower and upper quartiles - Whiskers from quartiles to extremes - Median, quartiles and whiskers labeled Return to Graph

Rally Coach—Practice!

Outcome 5, component 2, day 2 Create scatter plots, draw lines of best fit, interpret data from a scatter plot

Creating Scatter plots 1.Title and label the x and y axis on your coordinate plane (Make sure the x-axis is the independent or controlled variable. Y-axis is the dependent or ‘results’ variable. 2.Graph the ordered pairs given

Drawing a line of best fit This is a line that does NOT connect all of the dots, but rather attempts to be in the center of all dots. You want as many points above as below the line. *Line of best fit does NOT always start with zero!

Example: Notice: -line does not touch every point -line does not begin at zero -line has a positive trend (rising upwards left to right)

Example 2: Notice: -line does not touch every point -line does not begin at zero -line IGNORES the outlier -line has a negative correlation (slanting down left to right)

Example 3 What about this scatter plot? Can we draw a line of best fit? What kind of correlation is there?

Making predictions b When presented with a scatter plot, you can make conclusions. **You must draw your line of best fit BEFORE interpreting the info to be accurate. Why?

Cautions in using lines of best fit Don’t expect a best-fit line to give a good prediction unless the correlation is strong and there are many data points  If the sample points lie very close to the best-fit line, the correlation is very strong and the prediction is more likely to be accurate  If the sample points lie away from the best-fit line by substantial amounts, the correlation is weak and predictions tend to be much less accurate

2.Don’t use a best-fit line to make predictions beyond the bounds of the data points to which the line was fit Ex. ~ The diagram below represents the relationship between candle length and burning time. The data that was collected dealt with candles that all fall between 2 in. and 4 in. Using the line of best fit to make a prediction far off from these lengths would most likely be inappropriate. According to the line of best-fit, a candle with a length of 0 in. burns for 2 minutes, an impossibility

3.A best-fit line based on past data is not necessarily valid now and might not result in valid predictions of the future Ex. ~ Economists studying historical data found a strong correlation between unemployment and the rate of inflation. According to this correlation, inflation should have risen dramatically in the recent years when the unemployment rate fell below 6%. But inflation remained low, showing that the correlation from old data did not continue to hold. 4.Don’t make predictions about a population that is different from the population from which the sample data were drawn Ex. ~ you cannot expect that the correlation between aspirin consumption and heart attacks in an experiment involving only men will also apply to women 5.Remember that a best-fit line is meaningless when there is no significant correlation or when the relationship is nonlinear Ex. ~ there is no correlation between shoe size and IQ, so even though you can draw a line of best-fit, it is useless in making any conclusions

1.You’ve found a best-fit line for a correlation between the number of hours per day that people exercise and the number of calories they consume each day. You’ve used this correlation to predict that a person who exercises 18 hours per day would consume 15,000 calories per day. 2.There is a well-known but weak correlation between SAT scores and college grades. You use this correlation to predict the college grades of your best friend from her SAT scores. 3.Historical data have shown a strong negative correlation between birth rates in Russia and affluence. That is, countries with greater affluence tend to have lower birth rates. These data predict a high birth rate in Russia. State whether the prediction (or implied prediction) should be trusted in each of the following cases, and explain why or why not.

Answers: 1. This prediction would be beyond the bounds of the data collected and should therefore not be trusted 2. Since the correlation is weak, that means that there is much scatter in the data and you should not expect great accuracy in the prediction 3. We cannot automatically assume that the historical data still apply today. In fact, Russia currently has a very low birth rate, despite also having a low level of affluence.

Practice making predictions Daily Ice cream Sales If it was 20 degrees Celsius outside, about how much money could you expect in sales? (discuss)

Assignment Scatter Plot/Line of best fit worksheet *Put your name on it *Pencil only *Due next class period