Quartiles

Learning Objectives Define quartiles (Q1, Q2, Q3) and the interquartile range (IQR). Calculate the median (Q2) for datasets with both an odd and an even number of values. Determine the lower quartile (Q1) and the upper quartile (Q3) of a given dataset. Calculate the interquartile range (IQR) and explain its significance as a measure of spread. Identify the five-number summary (Minimum, Q1, Q2, Q3, Maximum) for a dataset. Use the 1.5 x IQR rule to identify potential outliers in a dataset. Ever wonder how you rank compared to others on a test or in a video game? 🤔 Quartiles are the statistical tool that divides everyone into four groups, showing you exactly where you stand! In this tutorial, you will learn how to find quartiles, which are values that split a set of data into...

TermDefinitionExample Median (Second Quartile, Q2)The middle value in a dataset that has been sorted in ascending order. 50% of the data is below the median, and 50% is above it.In the sorted dataset {2, 5, 8, 11, 15}, the median (Q2) is 8. Lower Quartile (First Quartile, Q1)The median of the lower half of a sorted dataset. It marks the 25th percentile, meaning 25% of the data falls below it.In the dataset {2, 5, 8, 11, 15}, the lower half is {2, 5}. The median of this half, Q1, is (2+5)/2 = 3.5. Upper Quartile (Third Quartile, Q3)The median of the upper half of a sorted dataset. It marks the 75th percentile, meaning 75% of the data falls below it.In the dataset {2, 5, 8, 11, 15}, the upper half is {11, 15}. The median of this half, Q3, is (11+15)/2 = 13. Interquartile Range (IQR)The rang...

Position of the Median (Q2) Position = (n + 1) / 2 For a dataset with 'n' values sorted in ascending order, this formula gives you the position of the median. If the result is a decimal (e.g., 4.5), you average the values at the positions on either side (e.g., the 4th and 5th values). Interquartile Range (IQR) Formula IQR = Q3 - Q1 To find the IQR, simply subtract the value of the lower quartile (Q1) from the value of the upper quartile (Q3). A larger IQR means the data is more spread out. Outlier Detection Rule Lower Fence = Q1 - 1.5 * IQR \\ Upper Fence = Q3 + 1.5 * IQR Any data point that falls below the Lower Fence or above the Upper Fence is considered an outlier. This is a standard method for statistically identifying extreme values.