Question

You should be able to answer the following questions after studying “Error Analysis of a

Statistical Sample”, found in the Appendices.

a) What is the difference between “random uncertainty” and “systematic uncertainty”?

Provide examples of each.

b) How do you calculate the uncertainty in a set of values that fluctuate randomly about

some mean value?

c) What is the formula for the standard deviation of a sample? What information does the

standard deviation of a set of data provide?

d) What is meant by the phrase “Confidence Interval”?

e) Why is standard deviation used in conjunction with calculating the mean (average) of a

set of data?

Answer 1

a)Random uncerainity  are statistical fluctuations (in either direction) within the measured data because of the precision limitations of the measurement device. Random errors are often evaluated through statistical analysis and may be reduced by averaging over an oversized number of observations .

Systematic uncertainity are reproducible inaccuracies that are consistently within the same direction. These errors are difficult to detect and can't be analyzed statistically. If a scientific error is identified when calibrating against a typical , applying a correction or correction factor to atone for the effect can reduce the bias. Unlike random errors, systematic errors can't be detected or reduced by increasing the amount of observations.

b) We calculate the uncertainity by calculating the standard deviation and variance for such a data.

c) The equation for standard deviation is be a

where is the mean, N is the total number of observations, 's are the observations.

Standard deviation (SD) is the measure of how spead out is the data is around the mean. it is a measure of the average distance between the values of the data in the set and the mean.

d) Confidence Interval is a probability that a population parameter will fall between two set of values. It can  be any number of probablity. The common being 99% and 95%.Statisticians use confidence intervals to measure uncertainty. A Confidence interval is a range of values that likely would contain an unknown population parameter.

e) We calculate the standard deviation with mean because it is an important feature of a dataset, which gives us the precision of the data set. Always physicsts wants a error interval to make sure the correctness of th experiment. Also the error interval given by he SD will help us to know the relative spread of the values of the data set from the mean.