Graphing Data Box and whiskers plot Bar Graph Double Bar Graph Histograms Line Plots Circle Graphs

Collecting and organizing data  Collecting and organizing data in a useful way allows you to incorporate many skills. Organizing data in tables will not only help you to disseminate data collected, but to perhaps find a solution to a problem or a reoccurring pattern. Make sure you are labeling and using correct scaling in graphical representation. This will aid in further data analysis and comprehension

Clusters, Gaps, and Outliers  A cluster is formed when several data points lie in a small interval.  A gap is an interval that contains no data.  An outlier has a value that is much greater than or much less than other data in the set. An outlier may significantly affect the mean of a data set. A single outlier will not affect the mode(s) and is likely to affect the median only slightly. Features such as clusters, gaps, and outliers are more easily seen when the data are shown on a line plot.

Clusters, Gaps, and Outliers

Mean, Median, Mode with outlierwithout outlier Mean Median32.5 Mode22

Box-and-Whisker Plots  A box-and-whisker plot can be used to show how the data in a set are distributed. To make a box-and-whisker plot, first order the data from least to greatest. Five measures need to be computed in order to make the plot. These are the lower extreme, the upper extreme, the lower quartile, the upper quartile, and the middle quartile.

Quartiles  The lower and upper extremes are the least and the greatest numbers respectively in the data set.  The middle quartile is the median of the data set.  The lower quartile is the median of the lower half of the data set. When a data set has an odd number of entries, the lower quartile is the median of the data that fall below the middle number of the set.  The upper quartile is the median of the upper half of the data set. When a data set has an odd number of entries, the upper quartile is the median of the data that fall above the middle number of the set. The three quartiles divide the data set into four parts.

Box-and-Whisker Plots  The box-and-whisker plot is drawn using the five measures computed. It summarizes the data and makes it easy to see where the data are spread out and where they are closer together.  Example:  Make a box-and-whisker plot for the data set below. 60, 63, 69, 71, 73, 82, 87, 89, 92, 96, 99

60, 63, 69, 71, 73, 82, 87, 89, 92, 96, 99

Make another box and whiskers plot  Use the following set of data 41, 52, 57, 79, 72, 20, 39, 23, 59, 76, 43

Bar Graphs and Histograms What do you know about:  bar graph?  double bar graph?  Histogram?

Bar Graph  A bar graph can be used to display and compare data  The scale should include all the data values and be easily divided into equal intervals.

How to interpret a Bar Graph?  How many of Ms. Smith’s students are band members?  How many of Ms. Smith’s students are not band members?

Double Bar Graph  Can be used to compare two related sets of data

How to make a Double-Bar Graph?  Choose a scale and interval for the vertical axis.  Draw a pair of bars for each country’s data. Use different colors to show males and females.  Label the axes and give the graph a title.  Make a key to show what each bar represents.

The table shows the highway speed limits on interstate roads.within three states RuralUrbanState 70 mi/h65mi/hFlorida 70 mi/h Texas 65 mi/h55mi/hVermont

Step 1  Choose a scale and interval for the vertical axis. RuralUrbanState 70 mi/h65mi/hFlorida 70 mi/h Texas 65 mi/h55mi/hVermont

Step 2  Draw a pair of bars for each state’s data. Use different colors to show urban and rural. RuralUrbanState 70 mi/h65mi/hFlorida 70 mi/h Texas 65 mi/h55mi/hVermont

Step 3 and 4  Label the axes and give the graph a title.  Make a key to show what each bar represents

Histogram  Histogram is a bar graph that shows the frequency of data within equal intervals.  There is no space in between the bars.

The table below shows the number of hours students watch TV in one week Make a histogram of all the data. Number of hours of TV 1II6III 2IIII7IIIII - IIII 3 8III 4 IIIII - I9IIIII 5 IIIII - III

Step 1  Make a frequency table of the data. Be sure to use equal intervals Frequency Number of hours of TV Number of hours of TV 1II6III 2IIII7IIIII - IIII 3 8III 4 IIIII - I9IIIII 5 IIIII - III

Step 2  Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency. Frequency Number of hours of TV

Step 3  Draw a bar for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.  Label the axes and give the graph title Frequency Number of hours of TV

Can you now make a bar graph, double bar Graph and a histogram? The list below shows the results of a typing test in words per minute. Make a histogram of the data. 62, 55, 68, 47, 50, 41, 62, 39, 54, 70, 56, 70, 56, 47, 71, 55, 60, 42

WHAT IS A LINE PLOT  A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer then 25 numbers. It is a quick, simple way to organize data.

MAKING A NUMBER LINE PLOT  Once data is collected it is then time to make a line plot.1. Determine the scale to be used. If the data is best described in 100's have the scale increase by hundreds, if all the data can fit on a scale 0-10 then make it  2. Next draw a horizontal line across the paper.  3. Break the line into EQUAL parts that will hold your scale.  4. List the data. Place an X over the correct number for each of the datum collected. If a number is repeated then place the X above the other.

Sample

READING THE PLOT  1. OUTLIERS-data values that are substantially larger or smaller then the other values. When possible, try to find an explanation for any outliers you may find. If this was a graph representing the height of everyone in the class this outliers is most likely the teacher. Although this is not a number line plot, it gives a visual description of an outlier. The value near the top right is spaced away from the rest of the data making it an outlier.  2.GAPS-large spaces between points. In the example above the space between the data and the outlier is considered a gap. In the example below a gap occurs between 10 and 13.  3.CLUSTERS-isolated groups of points. These are places on the number line where data is concentrated. On this number line a large cluster appears from 0-4.

Circle graphs A graph made of a circle divided into sectors. Also called pie graph.

Parts of a Circle Graph Graph Title – the title tells what the graph is representing. Sectors – Each sector is one part of the whole circle. Sector Labels – Each label tells what the sector represents 30% pepperoni 15% sauce 55% cheese

How to make a circle graph  Using a compass, draw a circle large enough to show all of your data.  Determine how many sectors you will need in your graph. You will need to know the percentages of the whole of your data. Try to make the sector sizes look as close to the percentage of the circle as the percentage of your data.  Label each sector and give your graph a title.

Survey your classroom for cafeteria favorites. Choose four different lunches and gather the data. Make a table to show data. Pizza10 Chicken8 Spaghetti5 Fish2

 You must now change the numbers to percentages. To do this, change each number to a fraction.  10/25 8/25 5/25 2/25  Then divide the numerator by the denominator.  10/25=.40 8/25=.32 5/25=.20 2/25=.08  Then multiply the answer by 100 .40*100=40% .32*100=32% .20*100=20% .08*100=8%  Now you are ready to draw your circle graph.

First you will need to divide your circle into approximate sectors to represent each percentage. Label each sector with the appropriate name and percentage. Pizza 40% Fish 8% Spaghetti 20% Chicken 32%

Finally, give your graph a title. Favorite Lunch Foods