Data and Measurements

Data

Data comes in two forms.

• Qualitative Data - Non-numerical data that describes properties. Stating the color of a substance or describing a reaction vessel as warm to the touch are examples of qualitative data.

• Quantitative Data - Numerical data that is obtained by using a tool. Determining the mass of a sample to be 4.53 g using a digital balance is an example of quantitative data.

The goal of data collection is to be as precise and accurate as possible.

• Precise measurements are close together when repeated under the same conditions. Tools with high precision are able to obtain the same measurement consistently.

• Accurate measurements are close to a true or theoretical value. Tools must be calibrated in order to accurately obtain measurements.

Measurements can have varying combinations of accuracy and precision.

• High accuracy, high precision - The goal of data collection.

• High accuracy, low precision - Multiple measurements have a wide range. The mean of the measurements, however, suggests the true value. 

• Low accuracy, high precision - Multple measurements have a small range. However, all of the measurements are far from the true value. Often, this is caused by a tool that is not calibrated correctly or the tool is used incorrectly.

• Low accuracy, low precision - Multiple measurents have a wide range AND the mean is far from the true value.

Absolute Uncertainty

Every measurement has an uncertainty associated with it. The absolute uncertainty of a measurement is the range in which the true value falls within. The uncertainty of a measurement is recorded as + after the measurement. For instance, the mass of a sample can be recorded as 3.56 + 0.01 g. This states that the actual mass of the sample is between 3.55 g and 3.57 g.

The type of measuring device dictates how the uncertainty is determined.

• Analog Tools - Tools that require the user to estimate a reading (e.g., thermometer, ruler or a graduated cylinder). For analog tools, the uncertainty is + ½ of the smallest division. For instance, a graduated cylinder with 1 cm3 divisions has an absolute uncertainty of + 0.5 cm3.

• Digital Tools - Tools that do not require the user to estimate (e.g., digital balance or a pH sensor). For digital tools, the uncertainty is + the smallest division. For a digital balance that measures to 3 decimal places (0.000), the absolute uncertainty is  + 0.001 g

Percentage Uncertainty

The percentage (%) uncertainty compares the absolute uncertainty to the measured value. A low % uncertainty suggests high precision in the measurement while a high % uncertainty suggests lower confidence in the measurement

Percentage Uncertainty = absolute uncertainty / measured value x 100%

Increasing the magnitude of the measured value decreases the percentage uncertainty of the measurement. In other words, there is more certainty (less uncertainty) when the measured value increases.

For example, if a volume of liquid is recorded as 43.0 + 0.5 cm3, the percentage uncertainty for the volume is:

Percentage Uncertainty = (0.5 / 43.0) x 100% = 1.2%

If the volume of a second liquid is recorded as 21.0 + 0.5 cm3, the percentage uncertainty for the volume is:

Percentage Uncertainty = (0.5 / 21.0) x 100% = 2.4%

The larger volume has a lower percentage uncertainty. This is an important concept to remember when measuring small quantities.

Measuring Mass

Digital balances are used to measure the mass of an object. The level of precision is based upon the number of decimal places, with a digital balance that measures to 1 decimal place (e.g., 0.1 g) being less precise than a digital balance that measures to 2 decimal places (e.g., 0.01 g).

Measuring Time

Time, in seconds, is commonly measured using stopwatches or other timing devices. Because of human reaction time of deciding to stop the timer and the movement time to actually stop the timer, the uncertainty of time is typically reported as + 1 s.