1. 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
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2. 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)
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3. Any measurement involves the interaction of following three components
Analyst
Sample
Method
ERROR
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4. True
Value
Observed Value
Difference between
Error
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5. 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.
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6. 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
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7. 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
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8. 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
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9. Instrumental errors Methodic errors Types of Determinant error
Operational errors
Personal error
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10. 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
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11. These types of errors obtained due to classical methods2
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
MnNH4PO  Mn2P2O7 +2NH3+H2O
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12. 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.
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13. 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 .
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14. 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
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15. 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
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16. 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
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17. 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
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18. 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)
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19. Mean:
The mean is the most widely used measure of the central value. It is denoted by ¯x
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20. 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)
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21. 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).
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22. 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
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23. Average Deviation
The average deviation (a.d.) or the mean deviation is the average of individual deviations
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24. Standard Deviation
It is defined as the square root of the mean of the squares of Individual deviations. Mathematically
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25. Variance: Square of standard deviation is called as Variance.
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26. Numerical problems
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27. Questions? Please
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28. Thank You For Kind Attention
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29. All the best
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