4 Interpreting Data

ISPS: INTERPRETING DATA KDPM & KPLI LECTURE NOTES

EXERCISE 1 Read the following data. Construct a visual representation that you think will communicate the information best. Our sun has a surface temperature of about 5538°C. The innermost planet is Mercury. It has a surface temperature of about 327°C. The next planet, Venus, has a surface temperature of about 482°C. Our home planet Earth is next. Its surface temperature is about 14°C. Mars is the fourth planet and its surface temperature is about -23°C. Jupiter comes after Mars. Jupiter has a surface temperature of about -151°C. Saturn is next with a surface temperature of about -184°C. Uranus is after Saturn. Its surface temperature is about -207°C. Next is Neptune whose surface temperature is about -223°C. Pluto is the outermost planet. It is so far away from the sun that its surface temperature has not been measured but it is estimated to be about -230°C. SSS, MPKS

SAMPLE VISUAL REPRESENTATION

Planet’s Position from Sun

Surface Temperature (°C)

1 2 3 4 5 6 7 8 9

Which is better? Why? SSS, MPKS

INTRODUCTORY INFORMATION • The first step in interpreting data is to decide what data you want to gather. This comes from the hypothesis you devise. • It is important to organize data for easy interpretation. Data tables and charts are usually used. Graphs are created from data tables to get a visual image of the observations which simplifies interpretation and drawing conclusions. SSS, MPKS

INTRODUCTORY INFORMATION • Two types of graph: – Bar graph for descriptive/discrete data (data from variables that will be counted) Eg. Brands of paper towels, types of wood, gender, days of the week, etc

– Line graph for continous data (data from variables investigated over time) Eg. Volume of water, height of ladders, units of clock time, mass of fruit etc.

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PRESENTATION OBJECTIVES You should be able to: • Construct a table of data • Construct a graph • Interpreting a graph (relationship between variables)

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CONSTRUCTING A TABLE OF DATA COMMON CONVENTIONS: • The MANIPULATED VARIABLE is recorded in the LEFT column, the RESPONDING VARIABLE is recorded in the RIGHT column. • When repeated trials are conducted, the RV column is divided into smaller column.DERIVED QUANTITY is recorded in one or more columns to the right of the RV column. • UNITS are included in the column heading. • The levels of the MV are ordered, SSS, MPKS usually from smallest to largest.

EXAMPLE OF TABLE OF DATA

TRIALS 1

COLUMN FOR MV

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2

3

COLUMN FOR RV

COLUMN FOR DERIVED QUANTITY

TABULATING DATA SKILLS CHECKLIST • • • • • • • • •

Does the title tell about the MV and the RV? Is the left column for the MV? Are the label and units given for the MV? Are the levels of the MV ordered? Is the right column for the RV? Are the label and units given for the RV? Is the RV column subdivided for repeated trials? Are the RV data correctly recorded? Are there additional columns for derived quantities? • Are the label and units given for the derived quantities? • Are the derived quantities correctly calculated? SSS, MPKS

CONSTRUCTING A GRAPH PROCEDURE • Draw a horizontal line (x-axis) and a vertical line (y-axis) • The MV is written on the x-axis. The RV is written on the y-axis. • Write the title of the graph. • A graph title may take these form: The Effect of the MV on the RV How Does the MV affect the RV? SSS, MPKS

PROCEDURE (CONT) • Determine interval scales for each axis.STEPS • Find the range of data (subtract the smallest value from the largest value)

7 12 22 37 46 55

• Divide the difference by the number of interval you want (to use/cover the entire graph area)

55 – 7 = 48

• Round up interval to an easy counting number eg. 5, 10, 2, 4 etc • Mark off intervals along the axis. Begin with an interval that is less than the smallest value to be plotted and continue until you have exceeded the largest value to be plotted. SSS, MPKS

48 ÷ 5 = 9.6 9.6 ≈ 10

0

10

20

30

40

50

60

PROCEDURE (CONT) • Plot data pairs as points on the graph. The point is represented as (x,y) or (MV,RV). • Connect the points or draw a best-fit line. • The rules are:

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• The line should be a straight line or a smooth curve. • All points should lie either on the line or very near to the line. • There should be approximately equal number of data points on either side of the line.

INTERPRETING A GRAPH PROCEDURE • Tell what happens to the RV as the MV changes. Eg: The temperature of water increases as the length of time it is heated increases

• For a curved line graph – – – – SSS, MPKS

Describe the relationship in two sentences. First describe the relationship until the curve changes direction. A change in direction of a line indicates a change in the relationships between the variables Then tell what the relationship is for the rest of the graph.

EXERCISE 2 Shown are several graphs with lines drawn through data points. Decide whether it is a best-fit line. If not, why?

• Too many data points on one side • Should be curved SSS, MPKS

• Some points too far from line • Should be curved (U shaped)

EXERCISE 2 (CONT.)

• Line is best-fit. Line seems to average the points.

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• Too many data points on one side. • Curved line should be lowered.

• Curve not smooth. A ‘J’ shaped smooth curve is best-fit.

EXERCISE 3 Draw best-fit lines for these points.

1

4 SSS, MPKS

2

5

3

6

SELF-CHECK EXERCISE 3

1

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5

3

6

EXERCISE 4 Write a statement of relationship between the variables for each graph.

The breaking point increases as the diameter of the rope increases.

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The number of letters recognized decreases as the distance from the chart increases.

EXERCISE 4 (CONT.)

The average number of tomatoes produced increased rapidly until a temperature of 19°C was reached. Above 19°C the average number of tomatoes produced declined rapidly. SSS, MPKS

The temperature of water steadily increases when heated for 7 minutes. After that the temperature stays about the same even though heating continues.

EXERCISE 5 Description of an investigation and the data collected are given below. Also given are a graph of the data, a best-fit line, and a statement of the relationship between the variables. You are to describe whether each has been properly prepared. If a section has not been correctly presented, Number 1 check what part is wrong. THE INVESTIGATION Y of sea 932 ear The sea otters in a otters 1 46 sheltered lagoon 940 were counted over a 42 1 number of years. 35 952 30 1 STATEMENT 26 962 The number of sea 1 otters in this location 972 SELF CHECK has been steadily decreasing since 1932

• Variables on wrong axis • Statement is ok

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• Line does not average points (all points above line)

EXERCISE 6 A description of an investigation and a table of data are given here. 2. Construct a graph 3. Draw a best-fit line 4. Write a statement of the relationship between the variables. THE INVESTIGATION An investigation was carried out to determine the relationship between the size of a car motor and the gasoline mileage.

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Size of Motor (horsepower ) 47 100 140 193 227

Average Kilometers per Liter of Gasoline 7.0 5.0 4.0 3.5 3.0

ANSWER EXERCISE 6

The number of kilometers per liter of gasoline decreases as the size of the motor increases. However, the decrease is slower for motors above 120 horsepower. SSS, MPKS

GRAPHING SKILLS CHECKLIST • • • • • • • • • •

Does the title communicate the MV and RV? Is the MV on the x-axis? Are the labels/units given for the MV? Is the scale on the x-axis appropriate to represent the values of the MV? Is the RV on the y-axis? Are the labels/units given for the RV? Is the scale on the y-axis appropriate to represent the values of the RV? Are the data correctly plotted? Is the line-of-best-fit appropriate? Is the graph done neatly?

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