- The distance between the means is equal to 8.
- The mean absolute deviation (MAD) for class A is equal to 2.
- The mean absolute deviation (MAD) for class B is equal to 2.
- Distance between the means = four (4) times the MAD.
- There is no overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.
<h3>What is a number line?</h3>
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
<h3>What is a line plot?</h3>
A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
<h3>What is a mean?</h3>
A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
Mathematically, the distance between the means of both classes A and B is given by:
Distance = Mean of class A - Mean of class B
Distance = 12 - 4
Distance = 8.
The mean absolute deviation (MAD) for class A is given by:
MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]
MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]
MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]
MAD A = 1/9 × [18]
MAD A = 18/9
MAD A = 2.
Also, the mean absolute deviation (MAD) for class B is given by:
MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]
MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]
MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]
MAD B = 1/9 × [18]
MAD B = 18/9
MAD B = 2.
Therefore, distance between the means = four (4) times the MAD.
Distance = Means × MAD
8 = 4 × 2.
In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.
Read more on line plot here: brainly.com/question/8989301
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