## interquartile range

### The interquartile range (IQR) is a statistical measure that represents the spread or dispersion of a dataset

The interquartile range (IQR) is a statistical measure that represents the spread or dispersion of a dataset. It is also used as a measure of variability, similar to the range.

To understand the interquartile range, it’s important to first know about quartiles. Quartiles divide a dataset into four equal parts. The first quartile (Q1) represents the 25th percentile, meaning it marks the point where 25% of the data falls below it. The second quartile (Q2), often referred to as the median, represents the 50th percentile, where 50% of the data falls below it. Finally, the third quartile (Q3) represents the 75th percentile, where 75% of the data falls below it.

The interquartile range is calculated by subtracting the value of Q1 from Q3 (IQR = Q3 – Q1). This range holds the middle 50% of the data and excludes the lowest and highest 25% of the data.

The IQR is often used as a measure of spread in skewed datasets or ones where extreme values may exist. It helps to identify the variability within the middle range of the data, ignoring outliers.

For example, consider a dataset of exam scores: 65, 70, 72, 75, 80, 82, 86, 90, 92.

To find the interquartile range, we first need to find the first quartile (Q1) and third quartile (Q3). Since we have 9 data points, Q1 will be the average of the 2nd and 3rd values (70 and 72): (70 + 72) / 2 = 71. Q3 will be the average of the 7th and 8th values (86 and 90): (86 + 90) / 2 = 88.

Now, we can calculate the interquartile range: IQR = Q3 – Q1 = 88 – 71 = 17.

Therefore, the interquartile range for this dataset is 17. It indicates that the middle 50% of the exam scores range from 71 to 88, while the lowest and highest 25% of the scores are ignored.

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