The data set that is more spread out is data set E because it has the highest standard deviation.
The correct answer is E.
To find the data set with the farthest distribution, we have to determine the standard deviation of each data set.
SET A:
2, 3, 3, 4, 4, 4, 5, 5, 6
[tex]Mean, x = \frac{2 + 3 + 3+4 + 4+ 4+5 + 5 + 6}{9} = 4[/tex]
deviation of each data from the mean = absolute value of mean minus each data
deviation of each data from the mean = 2, 1, 1, 0, 0, 0, 1, 1, 2
SET B:
3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10
[tex]mean, x = \frac{3+4+5+6+6+7+7+7+8+8+9+10}{12} = 6.7[/tex]
deviation of each data from the mean = 3.7, 2.7, 1.7, 0.7, 0.7, 1.7, 1.7, 1.7, 2.7, 2.7, 3.7, 4.7
SET C:
0.9, 1.0, 1.0, 1.1, 1.1, 1.1, 1.2, 1.2, 1.3
[tex]mean , x = \frac{0.9 + 1 + 1+ 1.1 + 1.1 + 1.1 + 1.2 +1.2 + 1.3}{9} = 1.1[/tex]
deviation each data from the mean = 0.2, 0.1, 0.1, 0, 0, 0, 0.1, 0.1, 0.2
SET D:
4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 8
[tex]mean, x = \frac{4 + 4+ 4+ 5+ 5+ 6+ 7+7+ 8 + 8 + 8}{11} = 6[/tex]
deviation of each data from the mean = 2, 2, 2, 1, 1, 0, 1, 1, 2, 2, 2
SET E:
2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10
[tex]mean, x= \frac{2+4+5+5+6+6+7+7+7+8+8+9+9+10}{14} = 6.6[/tex]
deviation of each data from the mean = 4.6, 2.6, 1.6, 1.6, 0.6, 0.6, 1.6, 1.6, 1.6, 2.6, 2.6, 3.6, 3.6, 4.6
The only two data sets with more deviation from the mean is set B and set E.
However, set E is more spread out than set B if you consider their first and last deviations from the mean.
set B = (3.7 ------ 4.7) and set E = (4.6 ---------- 4.6)
Thus, the data set that is more spread out is data set E because it has the highest standard deviation.
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