Accuracy and Precision Notes

Essential Question & Overview

  • Essential Question: How do you measure accurately and precisely?
  • Topic Focus: Measurement principles, definition and determination of accuracy, definition and determination of precision, step-by-step mathematical calculations for error and precision ranges, and rules for recording data.

Accuracy

  • Definition: Accuracy is a measure of how much a given measurement agrees with the standard (known) value for that specific measurement.
  • Key Characteristics:
    • Reflects closeness to the true or accepted standard value.
    • Example Values:
    • Accurate reading: 100.00100.00
    • Inaccurate reading: 48.8948.89

Guidelines for Taking Measurements

  • Measurement Precision Standard: Always record a measurement to the smallest known scale division (number) plus one additional estimated digit/number.
  • Data Integrity Rule: NEVER round data during collection or initial measurement steps.

Precision

  • Definition: Precision refers to how much a given set of repeated measurements of the same sample agree with one another or with their collective mean (average).
  • Key Characteristics:
    • Reflects reproducibility and consistency among multiple trial results.
    • Example Data Set: 6.16.1, 6.26.2, 6.36.3

Step-by-Step Mathematical Calculations

Calculating Precision

  1. Step 1 (Find Average): Calculate the mean (average) of the recorded measurements in the data set.
  2. Step 2 (Determine Range): Subtract the lowest measured value from the highest measured value to find the range:    Range=Highest Value−Lowest Value\text{Range} = \text{Highest Value} - \text{Lowest Value}
  3. Step 3 (Divide Range): Divide the calculated range by 22 to get the range uncertainty parameter:    Range Uncertainty=Range2\text{Range Uncertainty} = \frac{\text{Range}}{2}
  4. Step 4 (Express Precision): Format the final precision as the average plus or minus the range uncertainty:    Precision=Average±Range Uncertainty\text{Precision} = \text{Average} \pm \text{Range Uncertainty}

Calculating Accuracy (% Error)

  • Percent Error Formula:%Error=∣Actual Value−Measured Value∣Actual Value×100\% \text{Error} = \frac{|\text{Actual Value} - \text{Measured Value}|}{\text{Actual Value}} \times 100
  • Terminology Breakdown:
    • Actual Value: The standard, accepted, or known value.
    • Measured Value: The experimental or given value obtained during measurement.

Practical Application & Summary

  • Core Summary Rule: Accuracy measures how close a measurement is to the correct target answer, whereas precision measures how close multiple individual measurements are to each other.
  • Laboratory Data Logging Template:
    • Measurement units commonly recorded: density or concentration in g/mL\text{g/mL} or spatial dimensions using standard centimeter (cm\text{cm}) measuring scales.
    • Recorded data tables must track all trial measurements, calculated Average, calculated Precision (Average±Range Uncertainty\text{Average} \pm \text{Range Uncertainty}), and calculated Accuracy (%Error\% \text{Error}).