Unit 3 - StatisticsSPECIFIC OUTCOME: SOLVE PROBLEMS THATINVOLVE CREATING AND INTERPRETING GRAPHS,INCLUDING•BAR GRAPHS•HISTOGRAMS•LINE GRAPHS•CIRCLE GRAPHS
Achievement Indicators• DETERMINE THE POSSIBLE GRAPHS THAT CAN BE USED TO REPRESENT A DATA SET, AND EXPLAIN THE ADVANTAGES AND DISADVANTAGES OF EACH.• CREATE, WITH OR WITHOUT TECHNOLOGY, A GRAPH TO REPRESENT A DATA SET.• DESCRIBE THE TRENDS IN THE GRAPH OF A DATA SET.
Achievement Indicators• INTERPOLATE OR EXTRAPOLATE VALUES FROM A GRAPH.• EXPLAIN, USING EXAMPLES, HOW THE SAME GRAPH CAN BE USED TO JUSTIFY MORE THAN ONE CONCLUSION.• EXPLAIN, USING EXAMPLES, HOW DIFFERENT GRAPHIC REPRESENTATIONS OF THE SAME DATA SET CAN BE USED TO EMPHASIZE A POINT OF VIEW.• SOLVE A CONTEXTUAL PROBLEM THAT INVOLVES THE INTERPRETATION OF A GRAPH.
Warm-up: 5 minsSEE – THINK – WONDER •What do you see? •What do you think? •What do you wonder about?
What do Graphs Tell You?A graph is a way of expressing a relationship between two different variables.There are several types of graphs Line Graph Bar Graph Circle Graph (Pie Chart) Histogram
VariablesEvery scientific investigation has variables:• Variable: factor that changes in an experiment.• Independent variable: variable that is manipulated (changed) in an experiment.• Dependent variable: variable that is affected by the independent variable.Example: In an experiment where we are looking at the effect of the amount of sunlight on plant growth, since we are manipulating the amount of sunlight, it is the independent variable and the growth of the plant is the dependent variable.
Identify the Axes Y- Axis Dependent Variable(what is observed and measured) Independent Variable (what is changed by the scientist) X- Axis
DRY MIX One way to remember which data goes on which axis is the acronym DRY MIX. D.R.Y. M.I.X. D- Dependent M- Manipulated R- Responding I- Independent Y- Y-axis X- X-axis
Title Write an appropriate title for the graph at the top. The title should contain both the independent and dependent variables.
Scale Decide on an appropriate scale for each axis. The scale refers to the min and max numbers used on each axis. They may or may not begin at zero. The min and max numbers used for the scale should be a little lower than the lowest value and a little higher than the highest value. This allows you to have a smaller range which emphasizes the comparisons/trends in the data.
Scale •The Y-axis scale is from 0-100. •The largest value though is only 35.
Scale •The Y-axis scale is now from 0-40. •This does a better job emphasizing the comparisons between coins.
Intervals Look at your minimum and maximum values you set up for both the Y and X-axis. (For most bar graphs, the X-axis will not have numerical values.) Decide on an appropriate interval for the scale you have chosen. The interval is the amount between one value and the next. It is highly recommended to use a common number for an interval such as 2, 5, 10, 25, 100, etc.
IntervalsThe interval forthe Y-axis is 20. The X-axis does not have numerical data and does not need an interval.
Labels Both axes need to be labeled so the reader knows exactly what the independent and dependent variables are. The dependent variable must be specific and include the units used to measure the data (such as “number of drops”).
Create-a-Graph Online!Click here to use the online tool!
Line Graph• A line graph shows changes that occur in related variables.• The independent variable is generally plotted Y on the horizontal axis, or X-axis.• The dependent variable is plotted on the vertical axis, or Y-axis, of the graph. x
Creating a Line GraphIMPORTANT COMPONENTS OF A GRAPH1. Title: Tells the viewer what the graph is about.2. X-Axis - Independent variable - Evenly spaced units - Uses an appropriate scale3. Y-Axix - Dependent variable - Evenly spaced units - Uses and appropriate scale4. Data: Data can be plotted on the graph from a DATA TABLE5. Key: If there is more than one line on the graph, a key is needed.
Bar Graph• A bar graph is used to compare a set of measurements amounts or changes.
Circle Graph (Pie Chart)• A circle graph or pie chart is a divided circle that shows how a part of something relates to the whole.
Creating a Line GraphFind the:1. Title2. X-Axis3. Y-Axis4. Key
What is a Histogram?A histogram is like a bar chart, but there are some important differences . It can only be used to show continuous data It can only be used to show numerical data The data is always grouped.
Here is a histogram showing how quickly pupils could say their twelve times tables A histogram is made up of a series of bars or rectangles The area of each rectangle represent s the frequencyFor continuous data, the class of a classboundaries are written as part of interval.a continuous scale
Histograms Example The histogram is a tool for presenting the distribution of a numerical variable in graphical form. For example, suppose the following data is the number of hours worked in a week by a group of nurses:42 47 43 26 30 42 28 42 50 3938 35 37 48 39 36 45 41 72 5343 37 42 48 40 35 39 30 47 38
Histograms These data are displayed in the following histogram: 12 The data values are grouped 10 in intervals of width five hours. 35 The first interval includes the 35 8 values from 25 to less than 30 36 40 hours. The second interval 37 41The vertical 6 includes values from 30 to 37 42axis is less than 35 and so on. The 38 42 45frequency. So, 4 intervals are shown on the 38 42 47for example, horizontal axis. 39 42 47there are two 2 26 30 50 39 43 48nurses who 0 28 30 39 43 48 53 72worked from 25 30 35 40 45 50 55 60 65 70 7525 to less than30 hours that Hours worked in the weekweek.
Histograms The choice of interval width will12 affect the appearance of the10 histogram.864 6 202 50 4 25 30 35 40 45 50 55 60 65 70 75 3 10 Hours worked in the week 2And here it is again, to the right,To the right is the same data 1presented in a histogram of interval 0 2.width 10. 0 26 25 30 34 35 38 42 46 45 50 54 55 58 62 65 66 70 74 75 Hours worked in the week Hours worked in the week
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 1 II 6 III 2 IIII 7 IIII - IIII 3 IIII - IIII 8 III 4 IIII - I 9 IIII 5 IIII - III
Make a frequency table of the data. Be sure to use equal intervals Number of Frequency hours of TV Number of hours of TV 1-3 151 II 6 III 4-6 172 IIII 7 IIII - IIII 7-9 163 IIII - IIII 8 III4 IIII - I 9 IIII5 IIII - III
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. 20Number of Frequency 16hours of TV 12 8 1-3 15 4-6 17 4 7-9 16 0 1-3 4-6 7-9
Draw a bar for each interval. The height of the bar is the Hours of Television Stepinterval. frequency for that 3 Watched Bars must touch but not overlap. 20 Label the axes and give the Number of students graph title 16 12 Number of Frequency 8 hours of TV 4 1-3 15 0 4-6 17 1-3 4-6 7-9 7-9 16 Hours
Using Circle Graphs to Represent DataAnother way to display data is in the form of acircle graph or pie chart. Circle graphs areuseful in displaying percentages, or parts of awhole.
Using Circle Graphs to Represent DataProperties of Circle Graphs: • They are 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.
Constructing Circle GraphsWhen constructing a circle graph, follow the steps below1. Is the Data Suitable--Determine if there is a "whole" for the data. Then determine what the different parts, or data groups, of the whole are.2. Calculate Percentages--For data that is not already given as a percentage, convert the amounts for each part, or data group size, into a percentage of the whole.3. Draw the Graph--Draw a circle and draw in a sector for each data group.4. Title and Label the Graph--Label the sectors with the data group name and percentage. Then add a title to the graph. This is the same as the title of the table.
Constructing Circle Graphs - ExampleConstruct a circle graph for the following data.
Constructing Circle Graphs - ExampleStep 1 – Is the Data Suitable?• There are five parts to the whole. Each data group is a category of sneaker brands (1) Adidas, (2) Nike, (3) Reebok, (4) Asics, (5) Other.Step 2 – Calculate Percentages• Calculate the whole: 150 + 192 + 60 + 108 + 90 = 600• Calculate the percentage for each part ex. Adidas: 150/600 = .25 or 25%
Constructing Circle Graphs - ExampleStep 3 – Draw the Graph• First, draw a circle. Then, draw in the sectors of the circle using a protractor to calculate the size of the sector.• The percentage has to be converted to a degrees. ex. 25% or .25 x 360o = 90oStep 4 – Title and Label the Graph
Can circle graphs be misleading? Classroom Activity: Page 118 - 119