Math and Arithmetic

What is a descriptive statistic?



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A descriptive statistic is a numerical summary of a dataset (e.g. a sample). There are four types of descriptive statistics that are commonly used: * Measures of central tendency: the central or most common value. # mean - There are several different types of mean, but by far the most commonly used is the arithmetic mean, which is simply the sum of the measurements divided by the number of measurements. This is typically what people refer to as the average. # median - value for which exactly half the measurements lie above and half below # mode - most frequently occurring measurement in a category

* Measures of variability: the normal spread of values around the central value. # standard deviation - the mean of the squared deviations from the mean. 1 standard deviation is the range around the mean in which roughly 62% of the values of data will fall. # quartiles, deciles, centiles - divide the values in the data set into equal quarters (or tenths, or hundredths) by number of data points, to show how the values of the data points cluster around the center. # correlation - (for two variables) how closely the distribution of values in the two variables are related.

* Measures of shape: what the data looks like. # skew - whether the data is balanced around the mean, or whether weighted towards one side or the other # kurtosis - the 'peaked-ness' or 'flatness' of a distribution.

* Measures of size: # sample size - how many points have been analyzed