Understanding Mean Answer Key

MATERIALS

• ball of string
• scissors
• meter stick or yardstick

Please work together in groups of at least four members.

DIRECTIONS

1. Use string to measure the length of a person's outstretched arm, from the tip of the middle finger to the shoulder. Mark the string. Beginning from the mark you just made from the end of the first person's arm length, measure the length of another group member's outstretched arm. Mark the string and repeat the process until everyone's arms have been measured on the same string.
2. Cut the string at the last mark. You now have one length of string that is equal to the combined lengths of all the arms in your group. Measure and record the entire length of the string.
3. Cut the string into equal-length sections so that there are as many sections as there are members of your group. Measure and record the length of one section.

QUESTIONS

1. What does the length of one section represent? (the mean)
2. Does it matter which student gets measured first and which last? (No, addition is commutative.)
3. If you add a new person to your group and repeat the steps, will your equal-length section be longer or shorter than your original equal-length section? (If the person's arm length is less than the arm length in Step 3, the new mean arm length will decrease. If the person's arm is longer, the mean will increase. If the person's arm is the same length as the mean, the mean stays the same.)
4. What calculations can you do to find the mean of any set of numbers? (Find the sum of the numbers and divide by the number of numbers.)

EXTENSION
If time permits, measure everyone's arm with the yardstick or meter stick. Add the values together and divide by the number of members in the group. Do you get the same value as your answer to question 3?

Return to worksheet Understanding Mean Activity Sheet

Return to lesson Investigating Median, Mode, and Mean