Experimental measurements usually have some uncertainty which can be introduced

Question

Experimental measurements usually have some uncertainty which can be introduced by random error or by systematic error (or bias) Random errors show up as differences in the measurement values, and the extent to which a set of measurements agree with one another is called the precision of the measurements. Systematic errors affect the accuracy of the measurement, and must be analyzed by calibrating the measurement with samples of a known value. Statistics presents a variety of ways of describing and analyzing these errors, and determining the confidence one can have that the "true value* lies within a certain range of values. The concept of standard deviation is a way of treating random errors that assumes the distribution of the total population of measurements follows a "normal" distribution curve (sometimes called a "bell curve") A set of measurements is usually only a sample of the total "population" of measurements that might be made, so the formulas in the right hand column above apply. You are asked to calibrate a 10-mL volumetric pipette by weighing to the nearest 0.1 mg the mass of water delivered by the pipette. You weigh six samples of water delivered by the pipette and convert the mass of each to volume by multiplying by the volume of 1.0000 g of water at 25°C (1.0040 mL). Following are your measurements: 10.0080 mL 9.9730 mL9.9870 mL 9.9720 mL 9.9590 mL 9.9860 mL Calculate the following statistical measures for this data Mean (i)-| 9.98083 | Variance (s3x 0.000284 Standard Deviation (s)0.0168

Explanation / Answer

The value of variance after rounding the last digit is correct but the system is showing it wrong. Another value of variance can be 0.000282.

Explanation

The value of standard deviation (s) is correct. We will use this value of standard deviation to calculate variance

Variance is square of standard deviation

variance = (standard deviation)2

variance = (0.0168)2

variance = 2.8224 x 10-4

or variance = 0.000282

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