Mode: This is the value that occurs most frequently. We find this by arranging all of the values from smallest to greatest, then identifying the middle value. Median: This is the “middle” value in the distribution. We find this by adding up all of the individual values, then dividing by the total number of values: Mean: This is the average value in the distribution. Three common measures of central tendency we can use are the mean, median, and the mode. Next, we want to describe where the center of the distribution is located. Since 22 is greater than 13.5, we can declare 22 to be an outlier. Using the Interquartile Range Calculator, we can input the 20 raw data values and find that the third quartile is 9, the interquartile range is 3, and thus any value above 9 + (1.5*3) = 13.5 is an outlier, by definition. One common way to formally define an outlier is any value that is 1.5 times the interquartile range above the third quartile or below the first quartile. From the histogram, we can visually inspect the distribution and see that 22 is potentially an outlier: Next, we want to determine if there are any outliers in the dataset.
It has one peak at the value “7.” Outliers Is the distribution unimodal (one peak) or bimodal (two peaks)? The distribution is unimodal. That is, the values aren’t skewed to one side or the other. Is the distribution symmetrical or skewed to one side? From the histogram, we can see that the distribution is roughly symmetrical. One helpful way to visualize the shape of the distribution is to create a histogram, which displays the frequencies of every value in the dataset: Shapeįirst, we want to describe the shape of the distribution. Here is how we can use SOCS to describe this distribution of data values. Suppose we have the following dataset that shows the height of a sample of 20 different plants.
#Socss form how to
Example: How to Use SOCS to Describe a Distribution Let’s walk through a simple example of how to use SOCS to describe a distribution. It stands for “shape, outliers, center, spread.” SOCS is a useful acronym that we can use to remember these four things. W hat is the range, interquartile range, standard deviation, and variance of the distribution?.What is the mean, median, and mode of the distribution?.
Are there any outliers present in the distribution?.Is the distribution unimodal (one peak) or bimodal (two peaks)?.Is the distribution symmetrical or skewed to one side?.In particular, there are four things that are helpful to know about a distribution: In statistics, we’re often interested in understanding how a dataset is distributed.
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