- The distance between the means is equal to 4.
- The mean absolute deviation (MAD) for player A is equal to 2.
- The mean absolute deviation (MAD) for player B is equal to 2.
- Distance between the means = two (2) times the MAD.
- There is some overlap and the distance between the means is between 1 times the MAD and 5 times the MAD.
What is a number line?
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.
What is a line plot?
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.
What is a mean?
A mean is also referred to as an 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 players A and B is given by:
Distance = Mean of player B - Mean of player A
Distance = 10 - 6
Distance = 4.
The mean absolute deviation (MAD) for player A is given by:
MAD A = 1/11[2(3 - 6) + 2(4 - 6) + (5 - 6) + (6 - 6) + (7 - 6) + 2(8 - 6) + 2(9 - 6)]
MAD A = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]
MAD A = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]
MAD A = 1/11 × [22]
MAD A = 22/11
MAD A = 2.
Also, the mean absolute deviation (MAD) for player B is given by:
MAD B = 1/11[2(7 - 10) + 2(8 - 10) + (9 - 10) + (10 - 10) + (11 - 10) + 2(12 - 10) + 2(13 - 10)]
MAD B = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]
MAD B = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]
MAD B = 1/11 × [22]
MAD B = 22/11
MAD B = 2.
Therefore, distance between the means = two (2) times the MAD.
Distance = Means × MAD
4 = 2 × 2.
In conclusion, we can infer and logically deduce that there is some 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: https://brainly.com/question/8989301
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