(1) 直徑均值 d_ = (d1+d2+d3+d4+d5)/5 = 20.01 (mm)
(2) 直徑數(shù)據(jù)均方差：(采用總體方差的有偏估計(jì),分母用樣本數(shù)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) 直徑的誤差表示：d = 20.01±0.02 mm
(4) 密度計(jì)算
球體體積 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) 誤差分析(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
∴ 相對(duì)誤差約：0.33%
絕對(duì)誤差：7.7853170 * 0.003305 = 0.026 ≈ 0.03(g/cm³)
(6) 確定密度的表達(dá)精度
根據(jù)絕對(duì)誤差,密度保留到小數(shù)點(diǎn)后二位
ρ = 7.79 ± 0.03 (g/cm³)