Statistical analysis A Statistical analysis of measurement data is common practice because it allows an analytical determination of the uncertainty of the final test result. This technique reduces the random error but can not reduce (remove) the systematic error. To verify this statistical analysis, we must define some arithmetic forms such as: Arithmetic mean. Average deviation. Standard deviation. Variance. Probable error. Limiting error.

Arithmetic Mean It is the most probable value of a measured variable. The best approximation will be made when the number of reading increase if x1, x2, ……, xn are the reading taken, then the arithmetic mean of these readings is given by: 1.4 where n is the total number of readings.

Average Deviation Deviation from the mean, d: Deviation is the departure of the given reading from the arithmetic mean 1.5 which may be positive or negative value. Average deviation The average deviation is an indication of the precision of the instruments used in making the measurements. The average deviation may be expressed as: 1.6

Standard Deviation,  1.7 For small number of readings (n < 30) the denominator is frequently expressed as n-1 to obtain amore accurate value for the standard deviation i.e.: 1.8

Variance (mean square error) Variance (V) = 1.9

Probable and Limiting Errors Probable error: It is the value of permissible error such that 50% of the measured data is suitable. The probable error ( r ) is defined as: r = ± 0.6745 σ Limiting Errors: An instrument is accurate within a certain percentage of a full-scale reading specified by the manufacturer, provided that he has perfectly accurate measurement. This is called limiting error or guaranteed error.

UNITS OF MEASUREMENTS In order to record or to compare magnitude of quantities, some one magnitude of each kind must be taken as basis or unit. Without unit the number of measure has no physical meaning. The basic three units are sufficient to describe all other phenomena in mechanical science are (Primary fundamental units) length (L), mass (M) and time (T). Measure of physical quantities in thermal, electrical and illumination science are also represented by fundamental units and called auxiliary fundamental units. All other units are expressed in terms of the fundamental units and are called derived units.

SYSTEM OF UNITS MKS UNITS. CGS EQUIVALENT UNIT. FPS EQUIVALENT UNIT. SI SYSTEM OF UNIT. SUPPLEMENTARY UNIT OF SI SYSTEM. SOME DERIVED UNITS IN SI SYSTEM.

CLASSIFICATION OF STANDARD A standard is a physical representation of a unit of measurement: INTERNATIONAL STANDARD. PRIMARY STANDARD. SECONDARY STANDARD. WORKING STANDARD.