**Precision**- A description of the reproducibility of results.
**Accuracy**- A description of the correctness of results.

High Precision, High Accuracy

Low Precision, High Accuracy

High Precision, Low Accuracy

**Error Types**- Random (Indeterminate)

Systematic (Determinate) - Bias, Instrumental, Personal, Method

**Absolute Error (E**_{a})- E
_{a}= X - x_{t}

where x_{t}is the accepted or true value

and X is the measurement or average of several measurements.

**Relative Error (E**_{relative})- E
_{relative}= (X - x_{t}) / x_{t}

- POPULATION
- All measurements of an observable. Infinate. (Impossible to get.)

- SAMPLE
- A subset of all the possible measurements. Finite. (Your results.)

- Sample Mean:

- Sample Standard Deviation:

## Calculation | ## Example | ## s |
---|---|---|

## Addition | ## x = p + q + r | |

## Multiplication | ## x = p q / r | |

## Exponentiation | ## x = p | |

## Logarithm | ## x = ln(p) |

Example:

- Prepare 10 ml of aqueous 1x10
^{-3}molar NiCl_{2}using a 10 (+/-0.1) ml volumetric flask and an analytical balance with an uncertainty of +/-0.001g. The formula weight of NiCl_{2}^{.}6H_{2}O is 237.70 (+/-0.01) g/mole. - Define: S = uncertainty, FW = formula weight, g = mass, M = molarity, and L = volume.
- Molarity = (g NiCl
_{2}^{.}6H_{2}O)/(FW NiCl_{2}^{.}6H_{2}O)/(L H_{2}O)

1x10^{-3}M = (g NiCl_{2}^{.}6H_{2}O)/(237.70 g/mole)/(0.010 L H_{2}O)

g = 0.002377 g NiCl_{2}^{.}6H_{2}O - What is the uncertainty in the molarity?
What is wrong with this procedure?

How could the uncertainty in the concentration be reduced?

This materil is very important in the laboratory. The linked table has information on uncertainties in laboratory glassware

Linear Regression in Microsoft Excel.

(If you use a blank and zero your instrument, (0,0) is a data point.)

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