第1次测量(j = 1)

平行样1 (i = 1)

平行样2 (i = 2)

平行样3 (i = 3)

最佳估计值(算术平均值)

醋酸浓度B_i1

$B_{11}=25.0\text{uL}/\text{L}$

$B_{21}=24.0\text{uL}/\text{L}$

$B_{31}=23.0\text{uL}/\text{L}$

$\overline{B_1}=24.0\text{uL}/\text{L}$

$B_{i1}-\overline{B_1}$

1.0

0

-1.0

n = 3

实验标准偏差

自由度

$s_1\left(B_1\right)=\sqrt{\frac{1}{n-1}{\displaystyle \sum _{i=1}^n{\left(B_{i1}-\overline{B_1}\right)}^2}}=1.0\text{uL}/\text{L}$

$v_1=n-1=2$

第2次测量(j = 2)

平行样1 (i = 1)

平行样2 (i = 2)

平行样3 (i = 3)

最佳估计值(算术平均值)

醋酸浓度B_i2

$B_{12}=22.0\text{uL}/\text{L}$

$B_{22}=22.0\text{uL}/\text{L}$

$B_{32}=24.0\text{uL}/\text{L}$

$\overline{B_2}=22.67\text{uL}/\text{L}$

$B_{i2}-\overline{B_2}$

−0.67

−0.67

1.33

n = 3

实验标准偏差

自由度

$s_2\left(B_2\right)=\sqrt{\frac{1}{n-1}{\displaystyle \sum _{i=1}^n{\left(B_{i2}-\overline{B_2}\right)}^2}}=1.1547\text{uL}/\text{L}$

$v_2=n-1=2$

第3次测量(j = 3)

平行样1 (i = 1)

平行样2 (i = 2)

平行样3 (i = 3)

最佳估计值(算术平均值)

醋酸浓度B_i3

$B_{13}=25.0\text{uL}/\text{L}$

$B_{23}=24.0\text{uL}/\text{L}$

$B_{33}=23.5\text{uL}/\text{L}$

$\overline{B_3}=24.17\text{uL}/\text{L}$

$B_{i3}-\overline{B_3}$

0.83

−0.17

−0.67

n = 3

实验标准偏差

自由度

$s_3\left(B_3\right)=\sqrt{\frac{1}{n-1}{\displaystyle \sum _{i=1}^n{\left(B_{i3}-\overline{B_3}\right)}^2}}=0.7638\text{uL}/\text{L}$

$v_3=n-1=2$

合并样本标准偏差

$s\left(B\right)=s_P\left(B\right)=\sqrt{\frac{{\displaystyle \sum _{j=1}^m{s}_j^2}}{m}}=\sqrt{\frac{{\left[s_1\left(B_1\right)\right]}^2+{\left[s_2\left(B_2\right)\right]}^2+{\left[s_3\left(B_3\right)\right]}^2}{3}}=0.9\text{861}\text{uL}/\text{L}$

自由度

$v={\displaystyle \sum _{j=1}^m{v}_j}=m{v}_j=6$

测量结果Ｂ的A类标准不确定度

$u_A\left(B\right)=u\left(\overline{B}\right)=s_P\left(B\right)/\sqrt{n}=0.5693\text{uL}/\text{L}$

B的算术平均值

$\overline{B}=\frac{1}{m}{\displaystyle \sum _{j=1}^m{B}_j}=\frac{1}{3}\left(24.0+22.67+24.17\right)=23.61\text{uL}/\text{L}$

B的A类相对标准不确定度

$u_{r,A}\left(B\right)=\frac{u_A\left(B\right)}{\overline{B}}=\frac{0.5693}{23.61}=0.02411$