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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
PictographPictograph
More Info
Fireflies
Day
s of
the
Wee
k
PictographPictograph
All pictographs All pictographs have a title.have a title.
Rows and Rows and columns shape columns shape the pictograph.the pictograph.
Label each row Label each row and column.and column.
Use pictures to Use pictures to show the data.show the data.
Each picture Each picture equals a certain equals a certain amount of data.amount of data.
Pictographs need Pictographs need a key.a key.
Return to Graph
Bar GraphBar GraphFavorite Subjects
010203040506070
Math Science Reading Social Studies
Subjects
Num
ber
of S
tude
nts
More Info
Bar GraphBar Graph The purpose of a The purpose of a
bar graph is to bar graph is to display and display and compare data. compare data.
Bar graphs use bars Bar graphs use bars to show the data.to show the data.
A bar graph must A bar graph must include: include:
- a title- a title
- labeled X and Y - labeled X and Y axesaxes
- equal intervals - equal intervals are used on the Y are used on the Y axisaxis
- the bars are - the bars are evenly spaced evenly spaced apart from each apart from each otherother
Return to Graph
Double Bar Double Bar GraphGraph
Plant Growth
0
5
10
15
20
Week 1 Week 2 Week 3 Week 4
Weeks
Inch
es Light Dark
More Info
Double Bar GraphDouble Bar Graph The purpose of a The purpose of a
double bar graph is double bar graph is to compare two or to compare two or more sets of data.more sets of data.
Uses bars to show Uses bars to show the data. the data.
Double bar graphs Double bar graphs must include: must include:
- Title- Title
- Labeled X and Y - Labeled X and Y axesaxes
- Equal intervals - Equal intervals are used on the Y are used on the Y axisaxis
- Pairs of bars are - Pairs of bars are equally spaced, equally spaced, but the compared but the compared bars are notbars are not
- Key- Key
Return to Graph
HistogramHistogram
10
9
8
7
6
5
4
3
2
1
10-Jan 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 90-99
Fre
quen
cy
Test Scores
Class Test Scores
More Info
HistogramHistogram
Histograms are Histograms are used to show the used to show the frequency of data.frequency of data.
Very similar to bar Very similar to bar graphs, but use graphs, but use intervals on the X intervals on the X axis.axis.
Bars do touch.Bars do touch.
Histograms have Histograms have a title.a title.
Histograms have Histograms have two axes which two axes which are labeled.are labeled.
Return to Graph
Line GraphLine GraphTemperature For One Week
0102030405060708090
100
Day 1 Day 2 Day 3 Day 4 Day 5
Days of the Week
Deg
rees
Far
enhe
it
More Info
Line GraphLine Graph
A line graph is A line graph is used to illustrate used to illustrate change over time.change over time.
Line graphs need:Line graphs need:
- Title- Title
- Labeled X - Labeled X and Y axesand Y axes
- Equal - Equal IntervalsIntervals
- Data - Data displayed by displayed by points connected points connected into lines into lines
Return to Graph
Double Line Double Line GraphGraph
Amount of Rainfall
0
1
2
3
4
5
May June July August
Months
Inch
es 1999
2000
More Info
Double Line GraphDouble Line Graph
A double line graph A double line graph is used to compare is used to compare two groups of two groups of related data over related data over time. time.
Double line graphs Double line graphs need:need:
- Title- Title
- Labeled X and Y - Labeled X and Y axesaxes
- Equal Intervals- Equal Intervals
- Data displayed - Data displayed by points by points connected into connected into lineslines
- Key- Key
Return to Graph
Circle GraphCircle GraphEye Color
40%
32%
20%
8%
BrownBlueGreenOther
More Info
Circle GraphCircle Graph
Circle graphs are Circle graphs are used to display used to display parts of the data parts of the data in relation to the in relation to the entire amount of entire amount of data.data.
All circle graphs All circle graphs need a title.need a title.
Each part is called Each part is called a sector and is a sector and is labeled.labeled.
All angles correct All angles correct (+2/-2 degrees)(+2/-2 degrees)
Return to Graph
Line PlotLine Plot
Favorite Colors
X
X
X X X
X X X X
X X X X X
X X X X X
Red Blue Green Yellow Purple
More Info
Line PlotLine Plot
A line plot shows the spread of all A line plot shows the spread of all the data on a number line.the data on a number line.
Easily identifies the mode.Easily identifies the mode. All line plots include: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 Stem and Leaf PlotPlot
12 7,8,8,9
13 1,2,4,4,4,6,6
14 0,0,2,3,3,4,7
15 1,1
Student Heights in Centimeters
Key: 12 7 = 127 cm More Info
7 8 8 9
1 2 4 4 4 6 6
0 0 2 3 3 4 7
1 1
Stem and Leaf PlotStem and Leaf Plot
Stem and leaf plots are used as a quick way Stem and leaf plots are used as a quick way of seeing how many pieces of data fall in of seeing how many pieces of data fall in various ranges. The reader can quickly tell:various ranges. The reader can quickly tell:
- the range- the range
- the mode- the mode Stem and leaf plots have a title, a stem, and Stem and leaf plots have a title, a stem, and
leavesleaves A key is used to explain how to read the A key is used to explain how to read the
stem and leaves. stem and leaves.
Return to Graph
Scatter PlotScatter PlotStudy Time Versus Grades
00
20
40
60 80100
1 2 3 4Study Time in Hours
Grade * *** * * *
5
More Info
Scatter PlotScatter Plot
Shows how closely Shows how closely two sets of data two sets of data are relatedare related
The closer the sets The closer the sets are related, the are related, the closer the points closer the points come to forming a come to forming a straight line.straight line.
Scatter Plots Scatter Plots include:include:
- title - title
- labeled axes- labeled axes
- equal intervals- equal intervals
- corresponding - corresponding numbers plotted numbers plotted as ordered pairsas ordered pairs
Return to Graph
Box - and - Whisker PlotBox - and - Whisker Plot
Hours of HomeworkHours of Homework
876
5
43 9
6.37.75
5
5.25 6.9
More Info
Box - and - Whisker Plot
Displays large set Displays large set of data.of data.
Gives general idea Gives general idea of how data of how data clusters.clusters.
Graph includes:Graph includes:
- Title- Title
- Labeled intervals- Labeled intervals
- Box between lower - Box between lower and upper quartiles and upper quartiles
- Whiskers from - Whiskers from quartiles to extremesquartiles to extremes
- Median, quartiles - Median, quartiles and whiskers labeled and whiskers labeled
Return to Graph
Rally Coach—Practice!Rally Coach—Practice!
Outcome 5, component 2, Outcome 5, component 2, day 2day 2
Create scatter plots, draw lines of best fit, interpret data from a scatter plot
Creating Scatter plotsCreating 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 fitDrawing a line of best fit
This is a line that does NOT connect all This is a line that does NOT connect all of the dots, but rather attempts to be in of the dots, but rather attempts to be in the center of all dots. You want as the center of all dots. You want as many points above as below the line.many points above as below the line.
*Line of best fit does NOT always start *Line of best fit does NOT always start with zero!with zero!
ExampExample:le:
Notice:Notice:
-line does not touch every -line does not touch every pointpoint
-line does not begin at zero-line does not begin at zero
-line has a positive trend -line has a positive trend (rising upwards left to (rising upwards left to right)right)
Example Example 2:2:
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 3Example 3
What about this What about this scatter plot?scatter plot?
Can we draw a line Can we draw a line of best fit?of best fit?
What kind of What kind of correlation is there?correlation is there?
Making Making predictionspredictions
When presented with When presented with a scatter plot, you a scatter plot, you can make can make conclusions. conclusions.
**You must draw your **You must draw your line of best fit line of best fit BEFORE interpreting BEFORE interpreting the info to be the info to be accurate. Why?accurate. Why?
Cautions in using lines of Cautions in using lines of best fitbest 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: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 Practice making predictionspredictions
Daily Ice cream Sales
If it was 20 degrees Celsius outside, about how much money could you expect in sales? (discuss)
AssignmentAssignment
Scatter Plot/Line of best fit worksheet
*Put your name on it*Pencil only*Due next class period