1. Statistical Treatment of Data Significant Figures : number of digits know with certainty + the first in doubt. Rounding off: use the same number of significant figures. Addition and subtraction: 13.4+ 1478.224 = 1491.624 ~ 1491.6 Multiplication and division: 31x350.1=10,853.1~11,000

2. Statistical Treatment of Data Kind of Errors: Systematic: instrument or the measuring technique. Random: judgement of the observer, fluctuations in conditions (temp., voltage, pressure, etc.)

3. Statistical Treatment of Data Absolute Error: Relative Error:

4. Statistical Treatment of Data Mean, arithmetic mean, and average are synonyms. Median: is the middle result when replicate data are arranged in order of size.

5. Statistical Treatment of Data Accuracy: indicates the closeness of the measurement to its true value or accepted value. It is expressed by the error. Precision: describes the reproducibility of measurements. That is: the closeness of results that have been obtained in exactly the same way.

6. Statistical Treatment of Data Low accuracy, high precision High accuracy, high precision Low accuracy, low precision High accuracy, low precision

7. Statistical Treatment of Data Distribution of Experimental Data Precision: Describes the reproducibility of measurements. It can be represented by the deviation from the mean. That is:

8. Distribution of Experimental Data Precision: Describes the reproducibility of the measurements. It can be represented by: The deviation from the mean. Average Deviation. Standard Deviation

9. Distribution of Experimental Data Standard Error of the Mean Provides limits within which there is a certain probability of finding the true value.

10. Distribution of Experimental Data The t-Distribution For small sample size (N<30) a correction is needed. The Student Distribution is similar to the normal (Gaussian) distribution but is spread out more.

11. Distribution of Experimental Data Biasing in the data collection or systematic error will not be detected by this type of statistical analysis. This type of statistical analysis only concerns itself with precision of values, NOT the accuracy.

12. Propagation of Error Uncertainty Analysis When the plus or minus notation is used to designate the uncertainty, the person making this designation is stating the degree of accuracy with which he or she believes the measurement was made. UNCERTAINTY

13. Propagation of Error Uncertainty Analysis 1. Suppose a set of measurements is made and the uncertainty in each measurement assessed with the same probability. 2. These measurements are used to calculate some desired result of the experiments. What is the uncertainty in the calculated result?

14. Propagation of Error Uncertainty Analysis is the uncertainty in the result. are the uncertainties in the independent variables.

15. Correlations and Correlation Coefficient Given data: Linear Regression using least squares analysis: attempts to minimize the sum of the vertical distances from the points to the straight line, that is: in particular,

16. Correlations and Correlation Coefficient Given data: But, we might equally well have written instead Then,

17. Correlations and Correlation Coefficient Given data: Correlation Coefficient= Perfect correlation No correlation