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

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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

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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.

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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

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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

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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)

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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

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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.

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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

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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