This document is a statistics exercise showing how to compute interquartile range, lower and upper bounds, and percentile rank for barangay population data in Valenzuela City. It walks through the formulas step by step and identifies outliers.
This document is a statistics exercise that demonstrates how to compute the interquartile range (IQR), lower and upper bounds, and percentile rank for a dataset of barangay populations in Valenzuela City. It is intended for students or anyone learning basic descriptive statistics and outlier detection.
The exercise begins by calculating the IQR using the formula IQR = Q3 - Q1, with Q1 at 5,973.5 and Q3 at 25,970, resulting in an IQR of 19,996.5. It then computes the lower bound (LB) as Q1 - 1.5(IQR) and the upper bound (UB) as Q3 + 1.5(IQR), yielding LB = -24,021.25 and UB = 55,964.75.
Using these bounds, the document identifies three outliers: Marulas, Ugong, and Gen. T. de Leon, all of which have populations above the upper bound. It notes that these barangays are significantly larger than most others in the dataset.
Next, the exercise calculates the percentile rank of Ugong's population using the formula PRS = 100(Y + 0.5(X)) / N, where Y = 30, X = 1, and N = 33, resulting in a percentile rank of 93% (rounded up).
The document concludes with an interpretation of the quartiles: Q1 indicates that 25% of barangays have 5,973.5 or fewer residents, Q2 (median) is 15,524, and Q3 shows that 75% have 25,970 or fewer. It notes that the data is widely dispersed with a large IQR, and the distribution is right-skewed due to the three outliers at the upper end.