Graph Worksheet



9TH GRADE SCIENCE: GRAPHING AND ANALYSIS OF SCIENTIFIC DATA

Graphing is an important procedure used by scientist to display the data that is collected during a controlled experiment. There are three main types of graphs:

Bar graphs (charts): Commonly used to compare quantities.

Line graphs (also called X-Y scatter plots): Use to show the change of one piece of information (dependent variable) as it relates to another change (independent variable).

Pie/circle graphs: Used to show parts of a whole.

Both bar and line graphs have an “X” axis (horizontal) and a “Y” axis (vertical).

PARTS OF A GRAPH:

Here is an example of a good X-Y scatter plot:

Graph 1: vA summary of the mean percentage change in mass in potato (Solanum Tuberosum) cylinders (n=4) submerged in sucrose solution [concentration (0 – 1.00 M)] for 24 h. Error bars represent standard deviation.

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Title: Summarizes information being represented in ANY graph. The title of a graph should always be “The dependence of [dependent variable] on [independent variable].” Another way this is commonly written is “The effect of [independent variable] on [dependent variable]” or in simplest form “ [dependent variable] vs [independent variable].”

Independent Variable: The variable that is controlled or defined by the experimenter, such as, time, dates, depth, and temperature. This is placed on the X axis.

Dependent Variable: The variable that is directly affected by the I.V. It is the result of what happens as time, dates, depth and temperature are changed. This is placed on the Y axis.

Choice of Scales

1. They should be sensible so that you can easily plot points or use them to read off values

2. Scales do not have to start at zero.

3. Choose an easy to read scale. 1 square/box = 1 or 2 or 4 or 5 or 10.

4. NEVER use an awkward scale such as 3 (or multiples of 3) and 7 or any other strange scale

such as 6 boxes = 10 or 7 boxes = 10.

5. Scales should be chosen to use the maximum amount of the graph in both directions.

6. Draw LARGE graphs. Scales should be chosen so that the plotted points occupy at least HALF of the graph grid in both the x and y directions.

7. Scales should be labelled reasonably frequently (there should not be more than three large squares between each scale label on either axis)

8. There should be no 'holes' in the scale (i.e. scale divisions must be regular).

Legend: A short descriptive narrative concerning the graph’s data may be placed under the graph.

BASIC DATA ANALYSIS

For any set of data, you often need to determine the following:

Mean: This is determined by adding all the numbers in a set of data and then dividing by the number of values.

Median*: This is the middle number in a set of data. If the there is an even set of numbers in the data, then take the average of the two middle numbers.

Eg: 2, 3, 4, 8, 12, 16, 20 median = 8

Eg: 3, 5, 8, 11, 17, 19, 27, 30 median is 11 + 17 = 28/2 = 14

Mode*: This is the number that occurs most often in a set of data.

Eg: 3, 4, 6, 6, 7, 9,9,9, 12, 12, 15 mode = 9

* To determine median and mode, the numbers in the set of data must be put in numerical order.

Extrapolate: extending the graph, along the same slope, above or below measured data.

Interpolate: predicting data between two measured points on the graph

BASIC GUIDELINES FOR DRAWING A LINE GRAPH (ALSO CALLED AN X-Y SCATTER PLOT)

Essential equipment

• a clear, see-through 30 cm plastic rule

• ALWAYS USE A RULER!

• a SHARP pencil (HB or B) - mechanical pencils are best

• an eraser

• ALWAYS use proper graph paper!

Recording Results

Tables and graphs should be checked for results that do not fit the pattern. Graphs (scatter plots) should be “best- fit” lines which do not have to include points that are obviously out of place but show the general pattern of results. Try to draw the points evenly scattered on either side of the line, which will usually be a straight line or a smooth curve.

Labelling of Axes & Graph

BOTH AXES to be labelled with the quantity and the correct unit.

The unit symbol may be placed under a solidus (a slash line) after the quantity (e.g. time / s) rather than placed inside a bracket.

The independent variable should always be graphed on the x-axis and the dependent variable on the y-axis. The independent variable is the quantity that is systematically changing on its own in equal increments (e.g. time) or is being defined and changed by the experimenter in a specific manner (e.g. 100 g more each time), while the dependent variable is the quantity that is being measured/ changing as a result of this systematic change of the independent variable. y changes when x changes and not the other way around. E.g., in a graph of age versus weight, weight changes with age not the other way round. Age goes on the x-axis and weight on the y-axis.

Plotting of Points

1. Plot points using a sharp pencil and using an X (NO thick 'blob' plots). Do NOT use a pen.

2. Plotted points need to be accurate to half a small square on the grid.

3. All measurements must be plotted (e.g. if ten measurements have been made then there must

be ten points). Do NOT omit points that do not fit the trend.

4. Points in the margin area (off the grid) are not allowed (they will be ignored when marked). This happens when a poor choice of scale was made. You need to start again and REDRAW the whole graph.

5. Units should always be drawn on both axes of the graph. A graph without units is useless.

6. The data in the graph should fill over half the page. If it doesn’t, rescale the axes so it does. The larger the area covered by the data, the more useful the graph will be as a predictive tool. Points should cover well more than half of the graph in both directions.

7. Scales should be chosen so that each square/box is an easy number to deal with or to estimate in between like 0.1, 0.25 0.5, 1, 2, 4, 5, 10, etc not something difficult like 3, 7, 9, etc.

8. Use a ruler! Draw your graph in pencil so that you can correct any errors.

9. NB: Graphs should always be shown as smooth lines or curves. Measurement of data is never perfect. Using data points (x’s not dots) as a guide for drawing smooth lines or curves rather than to indicate absolute truth is more useful for helping to identify the underlying trend in the values. NEVER connect the dots on purpose!!!

• Abrupt changes in a graph tell you that something significant has happened. Straight lines or smooth curves are usual on a graph. Obvious discontinuities suggest a significant change has taken place or that there has been a wrong measurement called an anomoly.

LINE (OR CURVE) OF BEST FIT (LOBF)

1. There must be AT LEAST five points on the graph grid for a 'best fit' line to be drawn.

2. Only one rogue/anomalous point (that does not fit the trend of the other plots) is allowed.

3. Use a sharp pencil and a long enough rule to draw the LOBF and draw a single thin line. A join in the line (two lines connected when drawn using a short ruler) is easily spotted when the page is viewed horizontally along the grid. A mechanical pencil gives a nice thin line. The line should be thinner than the thickest grid line. The points should be evenly scattered either side of the line of best fit.

4. Curves of best fit must be drawn smoothly. Turn the page around in order to draw the curve more comfortably.

5. ONE line of best fit must be drawn through the plots. NEVER JOIN THE DOTS ON PURPOSE!

6. There must be a reasonable balance of points on either side of the line (evenly spread). A clear plastic ruler should be used so you can see the points which are on both sides of the line as it is being drawn.

7. NEVER force a line through the origin (0,0). A LOBF is drawn according to YOUR plotted points.

8. Ignore any rogue/anomalous point that does not follow the general trend when drawing the LOBF. Circle it and write "discard" or "ignore" or “anomalous” next to it.

LINE GRAPHS SELF-ASSESSMENT RUBRIC

DIRECTIONS: Use this checklist to give yourself marks for your graph. For each criteria, award yourself:

● 2 marks if you met the specified criteria without making ANY major or minor mistakes

● 1.5 marks if you met the specified criteria but made one or two MINOR mistakes

● 1 mark if you met the specified criteria but made one or two MAJOR mistakes

● 0.5 marks if you made at least some attempt to meet the criteria but only partially succeeded

● 0 marks if you a) made little attempt to meet the specified criteria (and did not succeed) OR b) did not even try to meet the specified criteria

Marks awarded

|Criteria |You |Your teacher |

|1 - You have drawn the x- and y-axis with a ruler, and used most of the width and height of the space | | |

|available on your graph paper (including saving room for the axis labels). | | |

|2 - You have used a proper scale for the x- and y-axis, e.g., going up in 1s, 2s, 5s or 10s. When needed, | | |

|you have also included major/minor tick marks between your numbers. | | |

|3 - When needed, you have chosen starting points at the origin of the x- and y-axis that allow you to | | |

|maximize the available graph area. | | |

|4 - You have properly labelled both the x- and y- axes. When needed, you have included the appropriate SI | | |

|units (or their abbreviations) with each of your labels. | | |

|5 - You have plotted each point precisely and correctly. If done by hand, you have used a small, neat cross| | |

|(“x”) for each data point OR an appropriately sized dot (“●”). | | |

|6 - When needed, you have included raw data above the data points to assist readers. | | |

|7 - You have drawn proper lines to connect your data points - either by using a ruler to create a line | | |

|between each pair of points, or by drawing a well-positioned best-fit line. | | |

|8 - When needed, you have included a key (in case of the use of colored lines or different style data | | |

|points, e.g., “x”’s or “●”’s). Also, the key is placed in a location that is a) visible, b) logical, and c)| | |

|does not interfere with the reader’s attempts to interpret the graph. | | |

|9 - You have included a precise and informative title (or legend). | | |

|For example, the title/legend should include information related to the labels used for the x- and y-axis. | | |

|If the graph is about an organism, the scientific (latin) name should be used. Titles might also include | | |

|specific information regarding the location(s) and/or date(s) of the experiment. | | |

|10 - You have included a properly formatted data table so that the accuracy of your plotted data points can| | |

|be checked by others. | | |

|If the data table is NOT included, there should be a note below the graph that specifies its exact location| | |

|(e.g., “For data table, see lab notebook, p.16”). | | |

|Total Points Earned (out of 20 Total Points Possible) | | |

|- % conversion (divide your Total Points Earned by the Total Points Possible and then multiply that number | | |

|by 100) | | |

90-100% Exceeds expectations | Your work is excellent.

80-89% Meets expectations | Your work is good.

60-79% Approaches expectations | Your work meets some of the key criteria,

but it needs to improve.

30-59% Below expectations | Your work meets very few of the criteria.

0-29% Well below expectations | Your work meets almost none of the key

criteria. You need to read the criteria again, repeat the same task, and then make time to meet with your teacher.

• This rubric was adapted from a series of “Self-assessment check lists” published in Jones & Jones (2010), Cambridge IGCSE - Biology Workbook (2nd edition), Cambridge University Press: Cambridge, UK.

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