Measurement: errors, accuracy, and precision Chapter 6 Section 2 Measurement: errors, accuracy, and precision

Bell work Please put your book bag in the cubbie hole that belongs to your table. Take out a PENCIL or PEN and PAPER ASSIGNMENT Look at the picture. On your paper, answer the following questions: Two students measure the length of the same object. One reports a length of 3 m, the other reports a length of 10 m. Has one of them made a mistake? If the students reported measurements of 3 m and 3.01 m, do you think one of them has made a mistake?

Background info In this Investigate, you will measure a given distance by various techniques. You will have to determine which technique is best and why it is the best. You will also use estimation to decide if certain measurements are reasonable or not. A difference in measurement close to a certain accepted value is called an error. Physicists identify two kinds of errors in measurement. An error that can be corrected by calculation is called a systematic error. For example, if you measured the length of an object starting at the 1 cm mark on a ruler instead of at the end of the ruler, you could correct your measurement by subtracting 1 cm from the final reading on the ruler. An error that cannot be corrected by calculation is called a random error. No measurement is perfect. When you measure something, you make an approximation close to a certain accepted value. Random errors exist in any measurement. But you can estimate the amount of uncertainty in measurements that random errors introduce. Scientists provide an estimate of the size of the random errors in their data.  

Question and Hypothesis On your paper: Write a question that you think this lab investigation will answer Come up with a hypothesis (an educated guess that can be tested) on what you think would be the best way to measure a certain distance. For example, What would be the best way to measure the length of a football field if you didn’t know the yardage?

Investigation method a: STRIDE DISTANCE DISTANCE IN METERS GROUP 1 7.70 m GROUP 2 7.26 m GROUP 3 6.60 m GROUP 4 6.05 m GROUP 5 7.05 m GROUP 6 6.43 m GROUP 7 7.2 m GROUP 8 7.1 m GROUP 9 6.57 m GROUP 10 5.5 m GROUP 11 7.4 m GROUP 12 6.23 m

Investigation METHOD B: Ruler Distance METHOD A DISTANCE IN METERS GROUP 1 6.18 m GROUP 2 6.20 m GROUP 3 6.45 m GROUP 4 6.25 m GROUP 5 6.50 m GROUP 6 6.00 m GROUP 7 6.16 m GROUP 8 6.30 m GROUP 9 6.10 m GROUP 10 6.05 m GROUP 11 6.32 m GROUP 12 6.41 m

Discussion A difference in measurement close to a certain accepted value is called an error. Physicists identify two kinds of errors in measurement. An error that can be corrected by calculation is called a systematic error. For example, if you measured the length of an object starting at the 1 cm mark on a ruler instead of at the end of the ruler, you could correct your measurement by subtracting 1 cm from the final reading on the ruler. Subtract 1 cm from the final reading.

Discussion An error that cannot be corrected by calculation is called a random error. No measurement is perfect. When you measure something, you make an approximation close to a certain accepted value. Random errors exist in any measurement. But you can estimate the amount of uncertainty in measurements that random errors introduce. Scientists provide an estimate of the size of the random errors in their data.

Example of good estimate

Bell work CHECK FOR YOUR NEW SEAT!! Please put your book bag in the cubbie hole that belongs to your table. Take out a PENCIL or PEN Your Chapter 6 Section 2 Lab Packet Your binder for this class Your HW You DON’T need paper

CHAPTER 6 SECTION 2 Errors in measurement PHYSICS TALK CHAPTER 6 SECTION 2 Errors in measurement

Relating to the Investigation In the Investigate: The distance of the hallway was different when you used your stride as the length If you tried to improve the measurement by using a meter stick, you found that there were still differences in the measurement. You used the metric system to measure your data You converted the units There is no exact measurement In your measurement of the distance, you found different distributions of measurement.

Random errors Errors that cannot be corrected by calculating are called random errors It is the responsibility of the student scientist to record all the values of a measurement and recognize that the data will include random errors. The uncertainty will never be completely gone What does this mean? Example: Every time you measure the length of your desk, you might find that the measurement is different from a previous value by 0.1 cm. This difference could be in either direction (± 0.1 cm). You can use a more precise ruler and that may decrease this random error or uncertainty to only 0.05 cm (± 0.05 cm).

More about random errors Both the measuring tool and the person doing the measuring are responsible for the uncertainty. Centimeter ruler > uncertainty than Meter Stick with millimeters Be careful with alignment of ruler!!

histogram Histogram: a bar graph that shows how many data values fall into a certain interval. The number of data items in an interval is a frequency. The width of the bar represents the interval The height indicates the number of data items, or frequency, in that interval. The middle value is probably the “best guess” for the length of the hallway There will always be an uncertainty surrounding that value, as shown by the spread to the left and right of the middle value. If you made histograms of the length of a hallway using your stride (left figure), the meter stick (middle figure) or a tape measure (right figure), you can get a sense of the uncertainty in each type of measurement.

Systematic errors An error produced by using the wrong tool or using the tool incorrectly for measurement and can be corrected by calculation is called a systematic error. Systematic errors can be avoided or can be corrected by calculating. Example: If you mistake a yardstick for a meter stick and report your measurement as 4 m, when in fact it is 4 yd, that is a systematic error. Every measurement you record with that yardstick will have this error.

Accuracy Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm How close the measurement is to the true or actual value Example: Who is more accurate when measuring a book that has a true length of 17.0 cm? Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

Precision Which set is more precise? 18.2, 18.4 , 18.35 The exactness of a measurement Refers to how closely several measurements of the same quantity made in the same way can agree Example Which set is more precise? 18.2, 18.4 , 18.35 17.9 , 18.3 , 18.85 16.8 , 17.2 , 19.44

Accuracy and precision In shooting arrows at a target, you can have accuracy and precision by getting all the arrows in the bull’s-eye (left figure). You can have precision, but not accuracy by having all the arrows miss the bull’s-eye by the same amount (middle figure). You can also have accuracy, but without precision by having all the arrows surrounding the bull’s-eye spread out over the area (right figure). Notice that here the average position is the bull’s-eye (accuracy), but not one of the arrows actually hit the bull’s eye (precision).

Si system System we use to measure in Science Class SI is abbreviated from Le Système International d’Unités This is the system of units that is used by scientists. The system is based on the metric system. All units are related by some multiple of ten The meter (m) is the base unit of length. Other units are kilometer (km), centimeter (cm), and millimeter (mm). These three units are made up of the base unit meter and a prefix.

Driving the roads and united states units of measurement The United States does not use the metric system for everyday measurements. Distances along the road are measured in feet, yards, or miles. Speed limits are posted in miles per hour rather than kilometers per hour, as they are in many other countries. In this chapter, Driving the Roads, United States measurements will be used to express distances and speeds with respect to driving and traffic. In the classroom, you will use SI units for measuring.

Reflection on the Section and Chapter Challenge A measurement is never exact. When you make a measurement, you estimate that measurement. When a speed limit is 60 mi/h (about 100 km/h), you may find that sometimes you drive at 58 mi/h while other times you drive at 62 mi/h. These differences are random errors as you try to hold the speed constant. If a police officer stops you because you were driving at 75 mi/h (about 120 km/h) in a 30 mi/h zone, you will not be able to convince her that this was just an uncertainty in your measurement. Uncertainties in speeds may be something that you wish to include in your presentation or report.

Checking Up Explain the difference between systematic and random errors. Explain why there will always be uncertainty in measurement. What would the positions of arrows on a target need to be to illustrate measurements that are neither accurate nor precise?