G Currell & A A Dowman, Wiley-Blackwell, 2009

- You have a specific 10 mL automated pipette which is known to deliver volumes that have a
**true**mean value of 10.000 mL with a standard deviation uncertainty of 0.018 mL (≈ 0.18 %).

You use this same pipette**nine**times to deliver a total volume of about 90 mL.

See the worksheet ‘Q1’ in Excel file CombUncert01.xlsx.

Which is the most accurate way of describing the**total volume**:- 90.00 mL with a standard deviation uncertainty of 0.18% (i.e. 0.16 mL)
- 90.00 mL with a standard deviation uncertainty of 0.06% (i.e. 0.054 mL)
- 90.00 mL with a standard deviation uncertainty of 0.02% (i.e. 0.018 mL)

- In this idealised question, there is a range of 10 mL automated pipettes which have a tolerance (accuracy) of 1.0% (i.e. ±0.1 mL), but with
**perfect**precision of 0 % (i.e. there are**no random**variations within each pipette).

You select a**single**pipette at random and use it**nine**times to deliver a total of 90 mL.

See the worksheet ‘Q2’ in Excel file CombUncert01.xlsx.

Which is the most accurate way of describing the**final volume**:- 90 mL with a tolerance of 1.0% (i.e. ±0.9 mL)
- 90 mL with a tolerance of 0.33% (i.e. ±0.3 mL)
- 90 mL with a tolerance of 0.11% (i.e. ±0.1 mL)

- In this idealised question, there is a range of 10 mL automated pipettes which have a tolerance (accuracy) of 1.0% (i.e. ±0.1 mL), but with
**perfect**precision of 0 % (i.e. there are no random variations within each pipette).

You select nine**different**pipettes**at random**and use them to deliver a total of 90 mL.

See the worksheet ‘Q3’ in Excel file CombUncert01.xlsx.

Which is the most accurate way of describing the**final volume**:- 90 mL with a tolerance of 1.0% (i.e. ±0.9 mL)
- 90 mL with a standard deviation uncertainty of 0.33% (i.e. 0.3 mL)
- 90 mL with a standard deviation uncertainty of 0.20% (i.e. 0.18 mL)

- You have a specific 10 mL automated pipette which is known to have a
**standard deviation uncertainty**of 0.020 mL (≈ 0.20 %).

By weighing, you accurately measure the volumes delivered by this same pipette on 4 occasions, and calculate the mean,*v*_{1}, of these 4 values.

You then repeat the whole process several (*n*) times with the same pipette, and calculate the new mean value,*v*_{2},*v*_{3}…*v*, for each new set of 4 values._{n}

See the worksheet ‘Q4’ in Excel file CombUncert01.xlsx.

What value would you expect for the**sample standard deviation,**,*s*, of the mean values_{V}*v*_{1},*v*_{2},*v*_{3}…*v*?_{n}- 0.020 mL (≈ 0.20 %)
- 0.010 mL (≈ 0.10 %)
- 0.005 mL (≈ 0.05 %)

- You use four, different and
**randomly selected**, 10 mL automated pipettes to deliver a total volume of about 40 mL. The pipettes have a tolerance (accuracy) of 1.0% (i.e. ±0.1 mL), and a precision of 0.2% (i.e. 0.02 mL).

See the worksheet ‘Q5’ in Excel file CombUncert01.xlsx.

Which of the following gives the closest estimate for the**standard deviation uncertainty**in the total 40 mL volume.- 0.6%
- 0.5%
- 0.4%
- 0.3%