The interquartile range (IQR) measures how spread out the middle half of a dataset is. Find the first quartile (the 25th percentile, Q1) and the third quartile (the 75th percentile, Q3), then subtract: IQR = Q3 − Q1. Because it concentrates on the middle 50% of values, it reduces the influence of unusually large or small observations. section 2.15
Imagine bar tabs of 7, 18, 19, 20, 21, 22, 25, 120, and 1,500. The middle quartiles are Q1 = 19 and Q3 = 25, so the IQR is 6. In plain English, the central half of tabs falls from 19 to 25, even though a $1,500 tab sits far beyond that typical range. section 2.15
import numpy as np bar_tabs = [7, 18, 19, 20, 21, 22, 25, 120, 1500] q25 = np.percentile(bar_tabs, 25) q50 = np.percentile(bar_tabs, 50) q75 = np.percentile(bar_tabs, 75) # 19.0 21.0 25.0 print(q25, q50, q75)
Use NumPy’s percentile function to calculate Q1, the median, and Q3. Subtract the 25th-percentile result from the 75th-percentile result to obtain the IQR. section 2.15
Pair the IQR with the median when data are skewed. For tornado widths, the mean is about 215 yards while the median is 100 yards, reflecting a long right tail. The 25th and 75th percentiles—50 and 250 yards—show that the middle 50% spans 200 yards, a description less distorted by the widest tornadoes. section 2.20
import pandas as pd
import numpy as np
# Load the dataset
df = pd.read_csv("https://raw.githubusercontent.com/thomasnield/"
"training-data-repository/refs/heads/main/TORNADO_TRX.csv")
# Group by TOR_F_SCALE and calculate mean, median, standard deviation for TOR_WIDTH
grouped_stats = df.groupby('TOR_F_SCALE')['TOR_WIDTH'].agg(
p25=lambda x: np.percentile(x, 25), # 25th percentile (Q1)
median='median', # median
p75=lambda x: np.percentile(x, 75), # 75th percentile (Q3)
iqr=lambda x: np.percentile(x, 75) - np.percentile(x,25) # IQR
).reset_index()
# Round the results for readability
grouped_stats = grouped_stats.round(2)
# Print the results
print("TOR_WIDTH Statistics by TOR_F_SCALE:")
print(grouped_stats)
# TOR_WIDTH Statistics by TOR_F_SCALE:
# TOR_F_SCALE p25 median p75 iqr
# 0 EF0 30.0 50.0 100.0 70.0
# 1 EF1 80.0 150.0 300.0 220.0
# 2 EF2 200.0 400.0 792.5 592.5
# 3 EF3 400.0 700.0 1387.5 987.5
# 4 EF4 1000.0 1320.0 1575.0 575.0
# 5 EFU 20.0 30.0 50.0 30.0
For comparisons across categories, calculate Q1, median, Q3, and IQR separately with pandas groupby. This makes each tornado severity rating its own dataset for side-by-side spread comparisons. section 2.20
Quartiles are percentiles: the 25th, 50th, and 75th percentiles divide ordered data into four parts. Quantiles express the same idea on a 0-to-1 scale. Small datasets may require NumPy to interpolate percentile values, so check its estimation details when exact results matter. section 2.15
