The standard deviation measures the precision of a single typical measurement. It is common experience that the mean of a number of measurements gives a more precise estimation than a single measurement.
The standard deviation is directly related to precision of a procedure where low standard deviations are indicative of a high level of precision. There is not a necessary relation between standard deviation and accuracy except that a high level of accuracy requires low standard deviations.
So the standard deviation is a measure of the spread of your data, that is, the precision of your measurement.
If an instrument or method has good precision, 95% of values should fall within 2 standard deviations of the mean. That means that no more than 1 of the 20 results should fall outside of 2 standard deviations.
If you take more measurements, you are getting a more accurate picture of the spread. You shouldn't expect to get less spread--just less error in your measurement of a fundamental characteristic of the data.
The answer: Standard deviation is important because it tells us how spread out the values are in a given dataset. Whenever we analyze a dataset, we're interested in finding the following metrics: The center of the dataset. The most common way to measure the “center” is with the mean and the median.
The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.
A small standard deviation means that the values are all closely grouped together and therefore more precise. A large standard deviation means the values are not very similar and therefore less precise.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
The precision of a measuring tool is related to the size of its measurement increments. The smaller the measurement increment, the more precise the tool. Significant figures express the precision of a measuring tool.
The smaller the variance, the greater the precision. Precision is just an inverted variance τ=1/σ2.
Calculating Precision
Terms you will typically hear being used to describe precision in analytical chemistry are coefficient of variation (CV) and relative standard deviation (RSD). These are exactly the same thing and are a standardised way of measuring dispersion, the spread of your results.
Another way of considering the standard error is as a measure of the precision of the sample mean. The standard error of the sample mean depends on both the standard deviation and the sample size, by the simple relation SE = SD/√(sample size).
How Are Standard Deviation and Standard Error of the Mean Different? Standard deviation measures the variability from specific data points to the mean. Standard error of the mean measures the precision of the sample mean to the population mean that it is meant to estimate.
Accuracy is how close a value is to its true value. An example is how close an arrow gets to the bull's-eye center. Precision is how repeatable a measurement is. An example is how close a second arrow is to the first one (regardless of whether either is near the mark).
Other than these, temperature, pH, humidity, environmental noise and signals also interfere with the precision and accuracy of measurement.
Precision is determined by a statistical method called a standard deviation. Standard deviation is how much, on average, measurements differ from each other. High standard deviations indicate low precision, low standard deviations indicate high precision.
The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. The larger the standard deviation, the more variable the data set is.
As shown below, the larger the standard deviation, the more dispersion there is in the process data. All three processes above have a mean (average) of 10, but the standard deviations vary. A smaller standard deviation means greater consistency, predictability and quality.
If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.
Expert-Verified Answer. Accuracy is usually expressed in terms of percentage.
Standard deviation (SD) is a measure of imprecision. It indicates the variability or dispersion around the mean. Together, mean and SD determine acceptable ranges for a lot of control material. New control values must be calculated and acceptable ranges established for each new lot of control materials.