Satish Pradhan Dnyanasadhana College, Thane. Department of Chemistry S Satish Pradhan Dnyanasadhana College, Thane. Department of Chemistry S.Y.B.Sc. Analytical Chemistry Paper-I Sem-IV STATISTICAL TREATMENT OF ANALYTICAL DATA Dr.G.R.Bhagure 11/20/2018

STATISTICAL TREATMENT OF ANALYTICAL DATA 3.1.1 Errors in Chemical analysis: Types of errors-Determinate and Indeterminate errors-Constant and Proportionate errors, Absolute and Relative error-Minimization of errors 3.1.2 Measures of central tendency and dispersion : Measures of central tendency-Mean, Median, Mode. Measures of dispersion- Deviation, Average deviation, Relative average deviation ,Range , Standard deviation, Variance, Correlation coefficient and Relative standard deviation (Numerical problems expected) 11/20/2018

Any measurement involves the interaction of following three components Analyst Sample Method ERROR 11/20/2018

True Value Observed Value Difference between Error 11/20/2018

Types of Error Determinate error Indeterminate error Determinate error are those for which source can be observed or detected Indeterminate error The error are for which source can not be observed or not detected or can be pinpointed. 11/20/2018

No Source can be observed Sr. No. Characteristics Determinate error Indeterminate Error 1 Origin Source can be observed No Source can be observed 2 Magnitude Large Small 3 Direction Unidirectional No direction 4 Reproducibility Reproducible Not Reproducible 5 Effect Affect the measurement No Affect on measurement 6 Remedy Minimization possible, elimination in some cases possible No elimination 11/20/2018

Absolute error Relative error The difference between the measured value and True value Absolute error= xi -T Absolute error Absolute error / True value = xi –T/T Relative error 11/20/2018

Constant errors Proportionate errors The error in which the absolute error remains constant and the relative error changes with the change in sample size Constant errors The error in which the magnitude of the absolute error changes with change in sample size but relative error remains constant Proportionate errors 11/20/2018

Instrumental errors Methodic errors Types of Determinant error Operational errors Personal error 11/20/2018

Instrumental errors: Uncertainty in the last digit of the measurement due to least count of the instrument or volumetric glass ware. Ex. Counting /noting burette reading Improper response: Optimum condition for the working of the Instrument. Instrument works in that condition only. Ex. Working of glass electrode to measure pH using pH meter. pH of solution 1-10 can be recorded properly. If the solution is having pH greater than this range electrode system will give Improper response 11/20/2018

These types of errors obtained due to classical methods 2 Addition of excess amount of titrant 3 Incomplete reaction 4 Incomplete decomposition 5 Co-precipitation and post Co-precipitation 1 Solubility of salt These types of errors obtained due to classical methods as these methods involves no. of steps. Methodic Errors MnNH4PO4 ---- Mn2P2O7 +2NH3+H2O 11/20/2018

Operational errors Weighing of the hot crucible Loss of precipitate during filtration Blowing of last drop of in the nozzle of the precipitate Improper recording of the instrument Under washing or over washing of the ppt. Ignorance of temp. 11/20/2018

Personal error: The error due to physical limitation of the analyst and some time bias during measurement are called as Personal error. Ex. Colourblindnees of the person unable to detect end point . 11/20/2018

Minimization of errors Calibration of apparatus and Instruments Running Blank determination Use of Independent method of analysis Running control determination Running Parallel determination standard addition method Internal standard method Amplification method 11/20/2018

Calibration of apparatus and Instruments Operational and instrumental error can be minimized Calibration of apparatus and Instruments Methodic and operational errors can be minimized Running Blank determination Standard sub., Analysed and its result compared with the true value Deviation of the obtained result from the true or expected value will be measure of Methodic and operational errors Running of control determination 11/20/2018

Use of Independent method of analysis Analysis of same sample by two method of analysis ,one which will be chosen & results obtained can be compared. Methodic and operational errors can be different Use of Independent method of analysis Analysis of same sample by two different method by same analyst, or different . Methodic error will differ in two cases ,if same analyst Methodic and personal error will be differ in two cases if different analyst. Running Parallel determination Sample is analysed alone then sample + standard substance analysed Methodic and operational errors will be same for two measurements standard addition method 11/20/2018

Internal standard method Fixed amount of reference material is added to all standard solutions ,blank and sample . Ex. Na is added in the analysis of soil while determining lithium Internal standard method detector singles are amplified to rectify the improper response of detector. With the knowledge of type of error analyst can modify existing method, type of error and magnitude. Amplification method 11/20/2018

3.1.2 Measures of central tendency and dispersion : Measures of central tendency-Mean, Median, Mode. Measures of dispersion- Deviation, Average deviation, Relative average deviation ,Range , Standard deviation, Variance, Correlation coefficient and Relative standard deviation (Numerical problems expected) 11/20/2018

Mean: The mean is the most widely used measure of the central value. It is denoted by ¯x 11/20/2018

Median When quick measure of central value is to be decided and when gross errors are suspected the central tendency of a group of results can be expressed in terms of median by arranging the observations either in ascending or descending sequence. Median means the middle value. Ex. 1) 10.3,10.4, 10.5,10.7,10.8 (odd number of total observation the median is middle value i.e. 10.5) 11/20/2018

Mode The observation which occurs most frequently (i.e. which is repeated maximum number of times) in a series of observations is known as mode. For example, the mode of the set of data: 12,6, 12,7, 12.9, 12,7, 12.6, 12.8, 13.0, 12.5, 12.6, the value 12.6 is the mode since this is occurring with maximum frequency (three times). 11/20/2018

Deviation The error of a measurement can not be stated if the true value of the quantity is not known. It is meaningful then to take the difference between a particular measured value (observation) and the arithmetical mean of a series of measurements and this difference is called as its deviation for apparent error. A deviation is generally taken without regard to sign. It is defined mathematically as, d= Xi-X 11/20/2018

Average Deviation The average deviation (a.d.) or the mean deviation is the average of individual deviations 11/20/2018

Standard Deviation It is defined as the square root of the mean of the squares of Individual deviations. Mathematically 11/20/2018

Variance: Square of standard deviation is called as Variance. 11/20/2018

Numerical problems 11/20/2018

Questions? Please 11/20/2018

Thank You For Kind Attention 11/20/2018

All the best 11/20/2018