Question

Given Set \(P:\ 3,\ 4,\ 7,\ 8,\ 8\) and Set \(Q:\ 0,\ 0,\ 1,\ 1,\ 3,\ 7\).

Calculate the mean and mean absolute deviation for both sets. Then, answer the following questions.
1. How many data points in Set Q are closer than one mean absolute deviation from the mean of Set Q?
2. How many data points in Set P are further than two mean absolute deviations from the mean of Set P?
3. Find the difference between the two means. How does this difference relate to the mean absolute deviation of each set? For example, is it the same as the mean absolute deviation, twice as much, half as much, etc?

Answer 1

3 points ;

0 points

Explanation:

Given the data:

P: 3, 4, 7, 8, 8

Using a calculator :

Mean of set P = 6

Mean absolute deviation = 2

Q: 0, 0, 1, 1, 3, 7

Using a calculator :

Mean of set Q = 2

Mean absolute deviation = 2

1.)

1 mean absolute deviation (MAD) of set Q = 2

1 MAD from mean of Q : 2 ± 2 = (2 - 2) ; (2 + 2) = 0 ;4

Hence, points closer Than 1 MAD = 1, and 3

2.)

2 MAD of set P ; 2 * 2 = 4

2 MAD from. The mean :

(6 - 4) ; (4 + 6)

(2 ; 10)

No point in set P is further Than 2 MAD from the mean of Set P

3.)

Mean difference :

P - Q = 6 - 2 = 4

MAD difference :

2 - 2 = 0