Respuesta :
The difference between the mean of the two sets is 1, which is half the Mean absolute deviation.
What is mean absolute deviation?
The mean absolute deviation is the average distance between the data points and the mean of the data set.
A.) For the data set M, {0, 1, 3, 4, 7}, the mean and the mean absolute deviation can be written as,
[tex]\text{Mean of M}, (\mu_M) = \dfrac{0+1+3+4+7}{5} = 3[/tex]
The mean absolute deviation of the set M,
[tex]MAD = \dfrac{1}{n}\sum_{i=0}^{n}|x_i-m(x)|[/tex]
[tex]MAD = \dfrac{1}{5}\sum_{i=0}^{5}|x_i-m(x)|\\\\MAD_M= \dfrac{10}{5} = 2[/tex]
Now, since the MAD of the set M is 2, therefore, the data points in Set M that are closer than one mean absolute deviation from the mean are 3 because the range of the one mean absolute deviation from the mean,
Mean±MAD
= 3±2
= 3+2, 3-2
= 5, 1
Thus, the numbers coming between 1 to 5 are the data points that are closer than one mean absolute deviation which is 3{1, 3, 4}.
B.) For the data set N, {1, 2, 3, 4, 5, 9}, the mean and the mean absolute deviation can be written as,
[tex]\text{Mean of N}, (\mu_N) = \dfrac{1+2+3+4+5+9}{6} = 4[/tex]
The mean absolute deviation of the set N,
[tex]MAD = \dfrac{1}{n}\sum_{i=0}^{n}|x_i-m(x)|[/tex]
[tex]MAD = \dfrac{1}{6}\sum_{i=0}^{6}|x_i-m(x)|\\\\MAD_m= \dfrac{12}{6} = 2[/tex]
Now, since the MAD of the set N is 2, therefore, the data points in Set N that are further than two mean absolute deviations from the mean of Set are 3 because the range of the one mean absolute deviation from the mean,
Mean±2MAD
= 4±2(2)
= 4+4, 4-0
= 8, 0
Thus, the number not coming between 8 to 0 are the data points that are further than two mean absolute deviations from the mean of Set N which are 1{9}.
C.) The difference between the mean of the two sets is 1, which is half the Mean absolute deviation.
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