A mean is an arithmetic average of a set of observations. The set of population data that is the least dispersed from its mean is {6, 2, 2, 2}.
A mean is an arithmetic average of a set of observations. it is given by the formula,
[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]
To solve the problem we will find the mean of each population set and then add the difference between the mean and each data point.
A.)
[tex]Mean = \dfrac{2+3+2+9}{4} = \dfrac{16}{4} =4[/tex]
Dispersion of each point from the mean,
[tex]\rm |Mean - data\ point|\\|4-2|=2\\|4-3|=1\\|4-2|=2\\|4-9|=5[/tex]
Thus, the dispersion of the population from the means is 10 (2+1+2+5).
B.)
[tex]Mean = \dfrac{4+0+4+0}{4} = \dfrac{8}{4} =2[/tex]
Dispersion of each point from the mean,
[tex]\rm |Mean - data\ point|\\|2-4|=2\\|2-0|=2\\|2-4|=2\\|2-0|=2[/tex]
Thus, the dispersion of the population from the means is 8 (2+2+2+2).
C.)
[tex]Mean = \dfrac{6+2+2+2}{4} = \dfrac{12}{4} =3[/tex]
Dispersion of each point from the mean,
[tex]\rm |Mean - data\ point|\\|3-6|=3\\|3-2|=1\\|3-2|=1\\|3-2|=1[/tex]
Thus, the dispersion of the population from the means is 6 (3+1+1+1).
D.)
[tex]Mean = \dfrac{9+3+5+3}{4} = \dfrac{20}{4} =5[/tex]
Dispersion of each point from the mean,
[tex]\rm |Mean - data\ point|\\|5-9|=4\\|5-3|=2\\|5-5|=0\\|5-3|=2[/tex]
Thus, the dispersion of the population from the means is 8 (4+2+0+2).
Hence, the set of population data that is the least dispersed from its mean is {6, 2, 2, 2}.
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