Answer:
A.
Step-by-step explanation:
✔️Find the Mean and Mean Absolute Value of the first data set:
Write out the data values:
1, 2, 4, 4, 5, 5, 6, 7, 9, 9, 9, 11
Mean = sum of all data values ÷ number of data values in the data set
Mean = 72 ÷ 12 = 6
M.A.D = sum of |data value - mean| ÷ the number of data values
|1 - 6| = 5
|2 - 6| = 4
|4 - 6| = 2
|4 - 6| = 2
|5 - 6| = 1
|5 - 6| = 1
|6 - 6| = 0
|7 - 6| = 1
|9 - 6| = 3
|9 - 6| = 3
|9 - 6| = 3
|11 - 6| = 5
Sum of |data value - mean| = 30
M.A.D = 30 ÷ 12 ≈ 2.5.
✔️Find the mean and M.A.D of the second data set following the same steps and formula:
Write out the data:
1, 3, 4, 6, 6, 6, 7, 9, 9, 10, 10, 13
Mean = 84 ÷ 12 = 7
Sum of |data value - mean| = 32
M.A.D = 32 ÷ 12 = 2.7
✔️Comparing both data sets,
The difference of the means = 7 - 6 = 1
Thus, the value of this difference, 1, is less than half of the M.A.D of both sets, 2.5 and 2.7.
