Explain the difference between
(a) random and systematic error.
(b) constant and proportional error.
(c) absolute and relative error.
(d) mean and median.
Suggest two sources of systematic error and two sources of random error in measuring the width of a 3-m table with a 1-m metal rule.
Name three types of systematic errors.
The Correct Answer and Explanation is :
Difference Between Various Types of Errors and Statistical Measures
(a) Random and Systematic Error
- Random Error occurs due to unpredictable variations in measurement. These errors arise from environmental changes, observer inconsistencies, or instrument fluctuations. They can be reduced by taking multiple readings and averaging them.
- Systematic Error is consistent and occurs due to flaws in the measurement process, such as miscalibration of instruments or observer bias. These errors cannot be reduced by averaging but require corrections or better equipment.
(b) Constant and Proportional Error
- Constant Error remains the same regardless of the size of the measured quantity. An example is a ruler with an incorrectly marked zero point.
- Proportional Error varies with the measured value. For example, if an instrument consistently reads 5% higher than the actual value, the error increases as the measured value increases.
(c) Absolute and Relative Error
- Absolute Error is the difference between the measured value and the true value. It is expressed in the same units as the measurement.
- Relative Error is the ratio of the absolute error to the true value, usually expressed as a percentage. It provides a sense of how significant the error is relative to the measured value.
(d) Mean and Median
- Mean (Average) is the sum of all measured values divided by the number of observations. It is sensitive to extreme values.
- Median is the middle value in an ordered dataset. It is less affected by outliers and skewed data.
Sources of Systematic and Random Error in Measuring a 3-m Table with a 1-m Metal Rule
Systematic Errors
- Misalignment of the ruler – If the ruler is not placed in a straight line, the measurements will be consistently incorrect.
- Worn-out markings – If the ruler’s markings have faded, every measurement will have a consistent offset.
Random Errors
- Human perception error – Slight variations in eye alignment when reading the scale can cause fluctuations in measurements.
- Environmental factors – Changes in temperature may slightly expand or contract the metal ruler, affecting accuracy.
Three Types of Systematic Errors
- Instrumental Error – Caused by imperfections in measurement tools, such as incorrect calibrations.
- Observational Error – Due to the observer’s mistakes, such as incorrect parallax reading.
- Environmental Error – Caused by external conditions, like temperature or humidity affecting measurements.
Now, let me generate an image illustrating different types of errors.
Here is the educational infographic illustrating different types of measurement errors. Let me know if you need any modifications or explanations!
