Calculate the interquartile range of the data set. {7, 3, 10, 8, 4, 1, 8, 6, 5, 8}

Question:-Calculate the interquartile range of the data set. {7, 3, 10, 8, 4, 1, 8, 6, 5, 8}

Answer

To find the interquartile range (IQR), we first need to put the data in numerical order: {1, 3, 4, 5, 6, 7, 8, 8, 8, 10}. Now we are looking for the median that is in the middle. With 10 values, the median is the average of the 5th and the 6th data and it is 6. The lower quartile (Q1) is the median of the lower half of the data set: The value of Q1 is 4 because {1, 3, 4, 5}. The upper quartile (Q3) is the median of the upper half: {7, 8, 8, 8, 10}, thus, Q3 provides 8. The interquartile range (IQR) is the distance between upper and lower quartiles. In this regard, IQR = Q3 – Q1 = 8 – 4 = 4. The interquartile range for the given data is 4 . Measures the dispersion of the middle 50% of the data.