Random and Systematic Error Random Error Caused by

Random and Systematic Error

Random Error • Caused by unknown and unpredictable changes in the experiment • Changes may occur in the measuring instruments or the environmental conditions • Often follows a Gaussian model of distrubution

Random Error How to minimize random error: • Take more data • Errors can be evaluated through statistical analysis and can be reduced by averaging a large number of measurements

Systematic Error • Usually come from the measuring instruments, often because o there is something wrong with the instrument or its data handling system o the instrument is incorrectly used by the experimenter

Systematic Error • Two types of error can occur: o Offset or zero setting error, in which the instrument does not read zero when the quantity to be measured is zero o Multiplier or scale factor zero, in which the instrument consistently reads changes in the quantity to be measured that are greater or less than the actual changes

Systematic Error How to minimize systematic error: • Systematic errors are difficult to detect and cannot be analyzed statistically because all the data is off in the same direction • Spotting and sometimes correcting for systematic error takes a lot of care

Significant Figures

Rules 1. All nonzero digits are significant 2. Zeros between nonzero digits are significant 3. Leading zeros to the left of the first nonzero digits are not significant 4. Trailing zeros that are also to the right of a decimal point in a number are significant 5. Trailing zeros that are not to the right of a decimal point are not significant

Rules One way to determine if the zeros are significant: write the number in scientific notation. If you can or must get rid of the zeros, they are not significant.

Pacific-Atlantic Rule If the decimal point is present, count significant digits from the Pacific side of the number (left side); all digits after the first nonzero digit are significant If the decimal point is absent, count significant figures from the Atlantic side of the number (right side); all digits after the first nonzero digit are significant

Calculation Rules Multiplication and division: The result should be rounded so as to have the same number of significant figures as the number in the problem with the least number of significant figures Addition and subtraction: The result should be rounded to the last common digit occurring furthest to the right in all components, i. e. so that it has the same number of digits as the component with the fewest decimal places

Rounding Rules If the digit to be dropped is greater than 5, the last retained digit is increased by one. If the digit to be dropped is less than 5, the last retained digit is left as is. If the digit to be dropped is 5, and any digit following it is not zero, the last retained digit is increased by one. If the digit to be dropped is 5 and is followed only by zero is increased by one if it is odd, but left as is if it is even.