Errors in Measurements>Systematic Errors

When we measure any physical quantity (length, mass, time, temperature, etc.), the value we obtain is usually not exactly equal to its true value. The difference between the measured value and the true value is called measurement error.

A systematic error is an error that occurs in the same way every time a measurement is made.
It does not arise by pure chance; instead, it is caused by some fixed defect in the instrument, the method, or the observer.

Key characteristics:

• All readings are shifted in one direction (either all too high or all too low).
• The error is repeatable and of almost the same value every time under the same conditions.
• Systematic errors affect the accuracy (trueness) of the measurement.

Example: If a thermometer has its zero mark placed wrongly, it may always read 2 °C higher than the actual temperature.

Systematic errors can be grouped into three main types:

1. Instrumental errors
2. Errors due to imperfect experimental technique or method
3. Personal errors (observer errors)

Instrumental errors

These errors arise because the measuring instrument itself is faulty or badly calibrated.

Common causes:

• The instrument does not read zero when the quantity being measured is actually zero (zero error).
• The scale is wrongly marked or worn out.
• The pointer is bent or stuck and does not move freely.

Examples:

• The thermometer’s zero is not at the correct place, so all temperature readings are higher or lower than the true value.
• A laboratory balance shows some mass reading even when no weight is placed on it (zero error).
• An ammeter shows 0.5 A even when no current flows in the circuit.

Real-life example:

• A bathroom weighing scale always shows 2 kg more than your actual weight; every time you stand on it, your reading is systematically higher.

These errors occur when the procedure or setup of the experiment is incorrect, even if the instrument itself is good.

Common causes:

• The instrument is not placed in the proper position (e.g., not vertical, not horizontal).
• The method of measurement has a built-in flaw.

Examples:

• When measuring the volume of a liquid in a measuring cylinder that is not held vertically, the observed meniscus level will be wrong.
• Using a thermometer that does not make good thermal contact with the object, leading to consistently low temperature readings.

Real-life example:

• Always reading the water level in a tilted measuring jar will give the same type of wrong reading each time.

Personal errors are systematic errors introduced by the observer because of habits, bias, or carelessness.

Common causes:

• Consistently viewing a scale from an angle instead of directly from above (parallax error).
• Always choosing a particular way of estimating between two scale marks.

Example (parallax error):

• While measuring the length of an object with a ruler, if the eye is not placed vertically above the markings, the reading may always be a little more or a little less than the true length.

Real-life example:

• A student always reads the upper meniscus of a liquid instead of the lower meniscus, leading to consistently higher volume readings.

Systematic errors cannot be removed by simply taking many readings and averaging them, because the error is present in every reading in the same way.
However, they can be reduced or corrected by:

• Properly calibrating instruments (checking them against a standard and correcting zero errors).
• Using reliable, correctly set-up instruments and following standard laboratory procedures.
• Training observers to avoid personal bias and parallax, and to follow proper observation techniques.

If the magnitude and direction of a systematic error are known, it is often possible to apply a correction to the measured values.