Errors in measurement

Errors in measurement

1. Errors in Measurement (Sub: Measurement and Metrology) Code: BMEC0003 Instructor Mr. Gaurav Bharadwaj Assistant Prof. Department of ME GLA University

2. Cause of Errors As I discussed in previous lecture, main elements of Metrology are: Standard Work piece Instruments Persons Environment These five elements are also causes of errors in measurement because accuracy in measurement depends upon these elements.

3. Types of Errors There are three types of errors: Systematic errors Random errors

4. Systematic errors These types of errors occur due to any imperfection in the measuring instrument or use of measuring instrument in a wrong manner. These are of fixed magnitude. Nature of error is also fixed i.e. either positive or negative. Systematic Errors classified into three categories :- 1. Instrumental Errors 2. Environmental Errors 3. Observational Errors

5. Systematic errors Instrumental Errors: These errors arise due to faulty construction and calibration of the measuring instruments. Such errors arise due to friction in instruments. Lots of the time, the equipment being used is faulty due to misuse which changes the reading of the equipment. The zero error is a very common type of error. This error is common in devices like vernier calipers and screw gauge. The zero error can be either positive or negative. Sometimes the readings of the scale are worn off and this can also lead to a bad reading. Examples: Non uniform divisions on meter scale Instrument showing the reading initially from some value not from zero.

6. Systematic Errors Environmental errors: This type of error arises in the measurement due the effect of the external conditions on the measurement. The external condition includes temperature, pressure, and humidity, etc. Example: If you measure your temperature under the armpits and during the measurement if the electricity goes out and the room gets hot, it will affect your body temperature thereby affecting the reading.

7. Systematic errors Observational Errors: There are many sources of observational errors : Parallax, i.e. Apparent displacement when the line of vision is not normal to the scale . Inaccurate estimate of average reading . Wrong scale reading and wrong recording the data. Incorrect conversion of units between consecutive reading .

8. Here in Graph, Full Line shows the systematic Error in non Linear Instrument. While Broken Line shows response of an ideal instrument without Error.

9. Random errors The random errors are those errors, which occur irregularly and hence are random. These can arise due to random and unpredictable fluctuations in experimental conditions (e.g. unpredictable fluctuations in temperature, voltage supply, mechanical vibrations of experimental set-ups, etc, errors by the observer taking readings, etc . For example, when the same person repeats the same observation, it is very likely that he may get different readings every time.

10. Representation of Random errors

11. Statistical Analysis of Data Arithmetic mean: The best approximation that can be made of a number of readings of the same quantity is the arithmetic mean . It is also called Mean value . This mean is computed by summing all the values and dividing by the number of measurements.

12. Statistical Analysis of Data Dispersion from the mean: The property which denotes the extent to which the values are dispersed about the central value is termed as dispersion. It also known as spread or scatter. Let the distribution of income in our  random samples from year 2000 and 2015. We see that the two curves for the year 2015 and year 2000 have the same mean i.e 52, but the curve for year 2015 is more spread out as compared to that for year 2000. Thus , as compared to 2000, there were more people in 2015 with higher and lower incomes which validates our claim.

13. Statistical Analysis of Data There are certain terms which must be defined as they form the basis defining the measure of dispersion of data: 1. Range 2.Deviation 3.Average deviation 4. Standard deviation 5. Variance Range: The range of a data set gives the difference between the largest and smallest value.  Therefore, the range only takes the two most extreme values into account and tells nothing about what falls in the middle. Range = (Max. Value – Min. Value)

14. Statistical Analysis of Data Deviation : Deviation is departure of the observed reading from the arithmetic mean of the group of readings . Deviation = Mean Deviation: The  mean deviation gives us a measure of the typical difference (or deviation) from the mean.  If most data values are very similar to the mean, then the mean deviation score will be low, indicating high similarity within the data.   If there is great variation among scores, then the mean deviation score will be high, indicating low similarity within the data. Let Xi be the observed value of data point, X(bar) be the mean and N be the total data points.

15. Statistical Analysis of Data Standard Deviation  : The  standard deviation of a data set gives a measure of how each value in a dataset varies from the mean.  This is very similar to the mean deviation, and indeed, gives us quite similar information, substantively .  Let Xi be the observed value of data point, X(bar) be the mean and N be the total data points .

16. Thank you