解:由圖可知,小明5次成績?yōu)椋?,8,10,9,9;小兵5次成績?yōu)椋?,10,10,9,10。
小明成績的平均數(shù):$\overline{x}_1 = \frac{9 + 8 + 10 + 9 + 9}{5} = 9$
小明成績的方差:$s_1^2 = \frac{1}{5}[(9 - 9)^2 + (8 - 9)^2 + (10 - 9)^2 + (9 - 9)^2 + (9 - 9)^2] = \frac{1}{5}[0 + 1 + 1 + 0 + 0] = 0.4$
小兵成績的平均數(shù):$\overline{x}_2 = \frac{7 + 10 + 10 + 9 + 10}{5} = 9.2$
小兵成績的方差:$s_2^2 = \frac{1}{5}[(7 - 9.2)^2 + (10 - 9.2)^2 + (10 - 9.2)^2 + (9 - 9.2)^2 + (10 - 9.2)^2]$
$= \frac{1}{5}[(-2.2)^2 + (0.8)^2 + (0.8)^2 + (-0.2)^2 + (0.8)^2]$
$= \frac{1}{5}[4.84 + 0.64 + 0.64 + 0.04 + 0.64] = \frac{1}{5} × 6.8 = 1.36$
因為$0.4 < 1.36$,所以$s_1^2 < s_2^2$
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