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McGraw-Hill Math Grade 7 Answer Key Lesson 22.7 Mean Absolute Deviation
Exercises
CALCULATE
Sarah and Sadie recorded the numbers of points they scored in each of 5 basketball games.
Question 1.
What is Sarah’s average?
Answer:
4.6
Explanation:
Average = \(\frac{sum of the scores}{number of the scores}\)
= \(\frac{4 + 6 + 5 + 4 + 4}{5}\)
= \(\frac{23}{5}\) = 4.6
Question 2.
What is Sadie’s average?
Answer:
4
Explanation:
Average = \(\frac{sum of the scores}{number of the scores}\)
= \(\frac{3 + 7 + 2 + 6 + 2}{5}\)
= \(\frac{20}{5}\) = 4
Question 3.
What is the mean absolute deviation for Sarah’s scores?
Answer:
mean = 0.72
Explanation:
Sarah’s scores
Average = \(\frac{sum of the scores}{number of the scores}\)
= \(\frac{4 + 6 + 5 + 4 + 4}{5}\)
= \(\frac{23}{5}\) = 4.6
finding the difference between score and average score
I 4 – 4.6 I = 0.6
I 6 – 4.6 I = 1.4
I 5 – 4.6 I = 0.4
I 4 – 4.6 I = 0.6
I 4 – 4.6 I = 0.6
average of the differences =
= \(\frac{0.6 + 1.4 + 0.4 + 0.6 + 0.6}{5}\)
= \(\frac{3.6}{5}\) = 0.72
mean absolute deviation (MAD) = 0.72
Question 4.
What is the mean absolute deviation for Sadie’s scores?
Answer:
mean = 2
Explanation:
Sarah’s scores
Average = \(\frac{sum of the scores}{number of the scores}\)
= \(\frac{3 + 7 + 2 + 6 + 2}{5}\)
= \(\frac{20}{5}\) = 4
finding the difference between score and average score
I 3 – 4 I = 1
I 7 – 4 I = 3
I 2 – 4 I = 2
I 6 – 4 I = 2
I 2 – 4 I = 2
average of the differences,
= \(\frac{1 + 3 + 2 + 2 + 2}{5}\)
= \(\frac{10}{5}\) = 2
mean absolute deviation (MAD) = 2.
Question 5.
How many times greater is the mean absolute deviation of Sadie’s scores than for Sarah’s scores?
Answer:
1.28
Explanation:
the mean absolute deviation of Sadie’s score
mean absolute deviation (MAD) = 2
the mean absolute deviation of Sarah’s score
mean absolute deviation (MAD) = 0.72
The mean absolute deviation of Sadie’s scores than for Sarah’s scores difference,
= 2.0 – 0.72
= 1.28