Digits, Grade 8, Volume 2, Homework Helper

12-4: Additional Problem Solving

Part 1

Example Analyzing Deviations of Data Sets

The table shows the maximum lifespan of various animals. The mean absolute deviation is 48. Determine whether each statement is true or false.

  • a. The mean lifespan is 58 years.

  • b. The deviation of a dolphin's lifespan from the mean is +6.

  • c. The absolute deviation of a whale's lifespan from the mean is greater than the absolute deviation of a mouse's lifespan from the mean.

  • d. A cat's lifespan deviates from the mean more than average.

Solution

  • a. True.

    table with 3 rows and 2 columns , row1 column 1 , meanlifespan , column 2 equals . fraction 30 plus 24 plus 52 plus 65 plus 21 plus 4 plus 9 plus 26 plus 138 plus 211 , over 10 end fraction , row2 column 1 , , column 2 equals , 580 over 10 , row3 column 1 , , column 2 equals 58 , end table

  • b. False. The lifespan of a dolphin, 52 years, is less than the mean lifespan, 58 years, so the deviation is negative.

    52−58=−6

    The deviation of a dolphin's lifespan from the mean is −6.

  • c. True. The lifespan of a whale is 211 years.

    211−58 = 153

    So the absolute deviation of a whale's lifespan from the mean is 153.

    The lifespan of a mouse is 4 years.

    So the absolute deviation of a mouse's lifespan from the mean is 54.

    The absolute deviation of a whale's lifespan from the mean is greater than the absolute deviation of a mouse's lifespan from the mean.


End ofPage 429

Table of Contents

Digits, Grade 8, Volume 2, Homework Helper Unit D: Two-Dimensional Shapes Unit E: Measurement and Data Unit F: Personal Financial Literacy Unit G: Step-Up Lessons English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties