Statistical Process Control

Unit Overview
Measuring and Means
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Data Collection
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Statistical Process Control

Activity 1 (Student Copy)
Measuring and Means

Materials

  • rulers (cm)
  • calculators

Part A

1. When a precision measuring device gives a more specific measurement than that which is needed or the mean of several measurements results in a greater level of specificity than is needed, a measurement might be rounded to an acceptable larger unit or partial unit. Suppose you want to round 3.56 to the nearest tenth. Give your answer, and make any reasonable drawing that shows why your answer makes sense. Also explain in words why your answer is correct and how your drawing demonstrates this.


2. Round the following decimals to the nearest tenth.

A. 12.719 cm D. 8.02 cm
B. 0.97 cm E. 7 cm
C. 6.9 cm F. 0.6239 cm

3. Round the following decimals to the nearest hundredth.

A. 0.098 cm C. 0.19 cm
B. 4.63501 cm D. 15.6827 cm

4. Describe the procedure for rounding a decimal to a given place value (i.e., a "rounding rule").

Part B

1. Measure each coil to the nearest tenth of a centimeter.

A.
B.
C.
D.
E.


2. Use a calculator to find the mean length of the five coils to the nearest tenth of a centimeter.


3. Measuring from the left side of coil A and then from the left side of coil E, place a dot at the point that shows where the mean length of the five coils would fall. Use a straightedge to connect the two dots to create a vertical line extending from the top to the bottom coil.

  1. Use the vertical line, which represents the mean, to tell...
    ...which coils are longer than the mean:
    ...which coils are shorter than the mean:
    ...which coils are close to the mean:
  2. What could happen if you would "break off" the parts of coils that fall on the right side of your vertical line and place the pieces (breaking them further if needed) on the right ends of coils that are shorter than the mean (vertical line)?


4. Use a calculator to find the mean lengths of each of the following sets of coils to the nearest tenth of a centimeter. First estimate what you think the mean will be and tell why.

  1. 4.9 cm, 7.0 cm, 8.3 cm, 5.5 cm
    Estimated mean:

    Reason for estimate:
    Actual mean:
    Which lengths are longer than the mean?
    Which lengths are shorter than the mean?
    Which length is closest the mean?


  2. 3.6 cm, 6.6 cm, 9.1 cm, 6.2 cm, 5.7 cm
    Estimated mean:

    Reason for estimate:
    Actual mean:
    Which lengths are longer than the mean?
    Which lengths are shorter than the mean?
    Which length is closest the mean?


Extensions/Discussion Questions

  1. Try to find a different type of drawing from the one you used in Part A #1 to illustrate your answer.
  2. What does it mean to say a measurement is given to the nearest unit or partial unit (centimeter, inch, tenth of a centimeter, half inch, etc.)?
  3. When you round a number to a given place value or find a measurement to the nearest unit, between/among how many "closest" numbers must you choose? Explain.
  4. Why do you think we round up numbers that represent half (e.g., the 1/2 in 3 1/2 or the 5 in 6.5 when rounding to the nearest whole, or the 5 in 23.45 when rounding to tenths)?
  5. Why do you suppose that we often use a 0:
    • in the whole number place in a decimal such as 0.654?
    • in the tenths place for a number such as 5.0 that has been rounded to the nearest tenth?
    Could the 0 be omitted in each of these cases?


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Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.

Last updated on 1/30/1999
Comments: egalindo@indiana.edu
http://www.indiana.edu/~atmat/units/spc/proc_s1.htm