Just as we have a backup for the mean, which is the median, we also have a backup for standard deviation, which is the semi-interquartile range.

The semi-interquartile range is by definition half the distance between the 25th percentile and the 75th percentile.

Here is an example of a distribution of data that is divided into four equal-sized chunks. It might not look equal-sized but the area, shaded in pink, in each of those chunks is the same.

The first green line indicates the point at which all the scores are below 25% and the third green line indicates the point at which all scores are below 75%. The middle line is clearly 50%.

The distance between the 1st and 3rd lines is called the interquartile range (IQR). In this example, it is 2.69 units. Since this is a large deviation, we rather use the semi-interquartile range, which we achieve by dividing the answer by 2. This means that our range is 1.34 units.

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When working with a skew data set, why is better to use median and IQR rather than mean and standard deviation?

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