(1) 直径均值 d_ = (d1+d2+d3+d4+d5)/5 = 20.01 (mm)
(2) 直径数据均方差：(采用总体方差的有偏估计,分母用样本数n,而不是n-1)
S =√{[(d1-d_)²+(d1-d_)²+(d1-d_)²+(d1-d_)²+(d1-d_)² ]/5}
= 0.02(mm)
(3) 直径的误差表示：d = 20.01±0.02 mm
(4) 密度计算
球体体积 V = 4/3 * π * (d/2)³ = π*d³/6
密度 ρ = m/V = m/(π*d³/6)
= 6/π * m/d³ =7.7853170 (g/cm³)
(5) 误差分析(利用全微分)：
δρ = δ(6/π * m/d³)
= 6/π *[δm/d³ - 3m/d^4 *δd)
δρ/ρ = [6/π *[δm/d³ - 3m/d^4 *δd]/[6/π * m/d³]
= δm/m - 3δd/d
|δρ/ρ| =| δm/m - 3δd/d |
≤ | δm/m| +3|δd/d| = 0.01/32.66 +3*0.02/20.01=0.003305
∴ 相对误差约：0.33%
绝对误差：7.7853170 * 0.003305 = 0.026 ≈ 0.03(g/cm³)
(6) 确定密度的表达精度
根据绝对误差,密度保留到小数点后二位
ρ = 7.79 ± 0.03 (g/cm³)