Accuracy and precision Objective: To revise the baste statistics on sets of numb

Question

Accuracy and precision Objective: To revise the baste statistics on sets of numbers and to understand the difference between accuracy and precision. 1. Basic statistics on sets of numbers There is a saying among craftsmen, 'Measure thrice, cut once'. This means that you can reduce the risk of making a mistake in the work by checking the measurement a second or third time. 1.1 Getting the best estimate - taking the average of a number of readings If there is variation in readings when they are repeated, it is best to take many readings and take an average. An average gives you an estimate of the 'true' value. An average or arithmetic mean is usually shown by a symbol with a bar above it, e.g. x^bar ('x-bar') is the mean value of x. How many readings should you average? Broadly speaking, the more measurements you use, the better the estimate you will have of the 'true' value. The ideal would be to find the mean from an infinite set of values. the more results you use, the closer you get to that ideal estimate of the mean. But performing more readings takes extra effort, and yields 'diminishing returns'. What is a good number? As a rule of thumb usually between 4 and 10 readings is sufficient. 1.2 Spread - standard deviation The term refers to a statistical quantity that tells you how tightly your measurements are clustered around the mean value of your set of data. In other words, standard deviation is a good way to measure the spread of your data around the mean value. If the standard deviation is small then the spread is also small, which indicates that your data holds great around the average. The following equation is used to calculate the standard deviation: sigma _x = squareroot 1/n -1 sigma^n _i = 1 (x_1 - x^bar)^2 = squareroot (x_1 - x bar)^2 + (x_2 - x^bar)^2 + +(x_n - x^bar)^2/n -1 (1) The spread of values tells us something about the uncertainty of a measurement. By knowing how large this spread is, we can begin to judge the quality of the measurement or the set of measurements.

Explanation / Answer

Accuracy: it is defined as the average difference between mean value and all other measuements taken positive sign.

Precision: It is defined as the closeness of each measuremet, i.e. Upto what percentage our measurements are near to a given value.

For example: if true value is 9.54, and we have measurements of 9.4, 9.6 and 9.3

Then we measure again with another tool and get our data to be, 9.47, 9.59 and 9.39

Second tool has 3 significant figures hence it has better precision.

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