How is the interquartile range of a data set different from the standard deviation of a data set?
The IQR is often seen as a better measure of spread than the range as it is not affected by outliers. The variance and the standard deviation are measures of the spread of the data around the mean. They summarise how close each observed data value is to the mean value.
The interquartile range (IQR) and the standard deviation are both measures used to describe the spread or variability of a data set, but they quantify different aspects of it.
The interquartile range is a measure of the spread of the middle 50% of the data. To calculate the IQR, you need to first find the 25th percentile (Q1) and the 75th percentile (Q3) of the data set. The IQR is then obtained by subtracting Q1 from Q3.
On the other hand, the standard deviation measures the average amount by which each data point differs from the mean. It gives an overall sense of how much the data deviate from the average. To calculate the standard deviation, you need to follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data point, square the result, and sum these squared values.
3. Divide the sum by the number of data points minus one.
4. Take the square root of the result obtained in step 3.
The key difference is that the IQR focuses on the middle 50% of the data, while the standard deviation takes into account the entire data set. The IQR is less sensitive to extreme values or outliers because it only considers the spread of the data within the middle range. In contrast, the standard deviation considers the magnitude of each individual deviation from the mean, regardless of its position in the data set.