Accuracy precision and significant figures

accuracy,precision with examples. rules of rounding figures, significant figures

1. ACCURACY NEHLA P LECTURER MOULANA COLLEGE OF PHARMACY

2. DEFINITION The accuracy of a determination may be defined as the concordance between the data and the true or most probable value It is the agreement between the data and true value . it refers to the closeness of a single measurement to its true value. it is usually expressed in terms of error. Although the true value is usually not known, the mean calculated from results obtained from several different analytical methods which are very precise and in close agreement with one another may be considered the true value in a practical sense.

3. ABSOLUTE ERROR The difference between the mean and the true value is known as the Absolute error. RELATIVE ERROR The relative error is found by dividing the absolute error by the true value.Relative error is usually reported on a percentage basis by multiplying the relative error by 100 or on a parts per 1000 basis by multiplying the relative error by 1000. For Analytical methods these are two possible ways of determining the accuracy. They are 1.Absolute method 2.Comparative method

4.  1.Absolute method A synthetic sample containing known amounts of the constituents in question is used. These substances, primary standards, may be available commercially or they may be prepared by the analyst and subjected to rigorous purification by recrystallization, etc. The substances must be of known purity.

5. The test of the accuracy of the method under consideration is carried out by taking varying amounts of the constituent and proceeding according to specified instructions. The amount of the constituent must be varied, because the determinate errors in the procedure may be a function of the amount used. The difference between the mean of an adequate number of results and the amount of the constituent actually present, usually expressed as parts per thousand, is a measure of accuracy of the method in the absence of foreign substance.

6. 2.Comparative Method: Sometimes, as in the analysis of a mineral it may be impossible to prepare solid synthetic samples of the desired composition.  It is then necessary to resort to standard samples of the material in question (mineral, ore, alloy, etc) in which the content of the constituent sought has been determined by one or more supposedly "accurate" methods of a analysis. This comparative method, involving secondary standards, is obviously not altogether satisfactory from the theoretical standpoint, but is nevertheless very useful in applied analysis. Standard samples are issued by CDL.

7. PRECISION

8. DEFINITION Precision may be defined as the concordance of a series of measurements of the same quantity. The mean deviation or the relative mean deviation is a measure of precision. Precision is a measure of reproducibility of data within a series of results. Results within a series which agree closely with one another are said to be precise. Precise results are not necessarily accurate, for a determinated error may be responsible for the inaccuracy of each result in a series of measurements. Precision is usually reported as the average deviation, standard deviation, or range.

9. Precision is independent of accuracy. Precision is sometimes separated into: 1) Repeatability The variation arising when the conditions are kept identical and repeated measurements are taken during a short time period. 2)Reproducibility The variation arising using the same measurement process among different instruments and operators, and over longer time periods. Precision is a measure of the agreement among the values in a group of data, while accuracy is the agreement between the data and true value. In quantitative analysis the precision of measurements rarely exceeds 1 to 2 parts per thousand. Accuracy expresses the correctness of a measurement and precision the reproducibility of a measurement. Precision always accompanies accuracy, but a high degree of precision does not imply accuracy.

10. PRECISION MEASURES a) Ruggedness Tests Ruggedness tests describes the influence of small but reasonable alterations in the procedures of the quality of analysis. Examples of these minor variations are source and age of reagents, concentration and stability of solution and reagents, heating rate, thermometer errors, column temperature, humidity, voltage, fluctuation, variations of column to column, plate to plate, analyst to analyst and instrument to instrument and many others.

11. Arithmetic Mean The arithmetic mean is obtained by adding together the results of the various measurements and dividing the total by the number N of the measurements. In mathematical notation, the arithmetic mean for a small group of value is expressed as in which ∑ standing for the sum of X1. X1 is the individual measurement of the group, and N is the number of values. Median It is the central value of all the observations arranged from the lowest to highest. The Median is a value about which all the other are equally distributed. Half of the values are smaller and other half are larger than median value. The mean and median may or may not be the same.

12. Accuracy Precision Accuracy refers to the level of agreement Precision implies the level of variation that lies in the values of between the actual measurement and the several measurements of the same absolute measurement. factor. Represents how closely the results agree with Represents how closely results agree the standard value with one another Single-factor or measurement multiple measurements or factors are needed Results can be precise without being it is possible for a measurement to be accurate on occasion as a fluke. For a measurement to accurate. Alternatively, the results be consistently accurate, it should also be can be precise and accurate. precise. DIFFERENCE BETWEEN ACCURACY AND PRECISION

13. Significant Figures

14. DEFINITION The number of significant figures is the minimum number of digits needed to write a given value in scientific notation without loss of accuracy .

15. Rules for determining which digits are significant

16. Addition and Subtraction For addition and subtraction, the number of significant figures is determined by the piece of data with the fewest number of decimal places. For example, 100 (assume 3 significant figures) + 23.643 (5 significant figures) = 123.643, which should be rounded to 124 (3 significant figures).

17. Multiplication and Division For multiplication and division, the number of significant figures used in the answer is the number in the value with the fewest significant figures. For example, 3.0 (2 significant figures ) 12.60 (4 significant figures) = 37.8000 which should be rounded off to 38 (2 significant figures).

18. Rules for rounding off numbers (1) If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13. (2) If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12. (3) If the digit to be dropped is 5, and if any digit following it is not zero, the last remaining digit is increased by one. For example, 12.51 is rounded to 13. (4) If the digit to be dropped is 5 and is followed only by zeroes, the last remaining digit is increased by one if it is odd, but left as it is if even.

19. For example, 11.5 is rounded to 12, 12.5 is rounded to 12. This rule means that if the digit to be dropped is 5 followed only by zeroes, the result is always rounded to the even digit.

20. Logarithms and Antilogarithms It is made of two parts: 1) whole numbers ( charecteristics ) not considered as significant figures 2) fractions ( mantissa ) considered as significant figures