Definition of Interquartile Range:
The interquartile range (IQR) is a statistical measure that provides insight into the dispersion or spread of a dataset. It represents the range of values within which the middle 50% of the data points fall. The IQR is often used alongside the median to analyze the variability and identify potential outliers in a set of numerical data.
Calculating the Interquartile Range:
The interquartile range is determined by finding the difference between the upper quartile (Q3) and the lower quartile (Q1) of a dataset. These quartiles divide the data into four equal parts, with each quartile representing 25% of the data.
The steps to calculate the interquartile range are as follows:
- Arrange the dataset in ascending order.
- Determine the position of the upper quartile (Q3) and the lower quartile (Q1) using the formulas:
- Q3 = (3N + 1)/4
- Q1 = (N + 1)/4
- If the positions obtained in step 2 are not integers, round them up to the nearest whole number to identify the indices of the corresponding values.
- Find the values at the positions obtained in step 3. These values represent Q3 and Q1.
- Calculate the interquartile range by subtracting Q1 from Q3:
- IQR = Q3 – Q1
Interpreting the Interquartile Range:
The interquartile range provides information about the spread and distribution of the dataset. A larger IQR indicates a greater spread, suggesting that the data points are dispersed over a wider range of values. Conversely, a smaller IQR indicates a narrower spread, implying that the data points are concentrated closer to the median.
The IQR also assists in detecting potential outliers. Outliers are data points that significantly deviate from the majority of the values in a dataset. Typically, values that are less than Q1 – 1.5 * IQR or greater than Q3 + 1.5 * IQR are considered outliers. These values may require further investigation to determine if they are due to errors, unusual circumstances, or represent genuine extreme observations.