Summary Statistics and Distributions with pandas

Before you chart anything, meet your data. The fastest introduction pandas offers is describe() — one line that hands back the count, average, spread, and range of every numeric column. But a handful of summary numbers can hide as much as they reveal, which is why the next move is a histogram to see the actual shape those numbers only hint at. Working from team run differentials in the bundled 2023 standings, you'll also pick up the single most useful habit in data analysis: checking the mean against the median.

This builds on Pandas for Sports Data. The data is the bundled sample_standings.csv (2023 MLB regular season, MLB Stats API, retrieved June 2026), so it runs offline.

1. Summarize every column in one line

   describe() is the first thing to run on any new table. Point it at a few numeric columns and read down the output.

   import pandas as pd
   
   df = pd.read_csv("sample_standings.csv")
   print(df[["W", "RS", "RA", "RunDiff"]].describe().round(1).to_string())

   describe() on wins, runs, and run differential

              W     RS     RA  RunDiff
   count   30.0   30.0   30.0     30.0
   mean    81.0  747.7  747.7      0.0
   std     13.1   82.9   82.1    139.9
   min     50.0  585.0  647.0   -339.0
   25%     75.2  680.0  697.2    -87.2
   50%     82.0  742.5  721.0    -13.5
   75%     89.8  792.8  813.2    102.8
   max    104.0  947.0  957.0    231.0

   Each row is a question answered. count confirms all 30 teams are present (no missing rows). mean and std give the center and spread — wins average 81 (half a 162-game season, as they must) with a standard deviation of about 13. min, the quartiles (25%/50%/75%), and max trace the range: run differential runs from −339 all the way to +231.

2. The habit that catches skew: mean vs. median

   Look closely at run differential. The mean is 0.0 — which has to be true, since every run scored by one team is a run allowed by another, so league-wide they cancel. But the median (the 50% row) is about −13.5. When the mean sits well above the median, the distribution is right-skewed: a few exceptional values are pulling the average up.

   mean = df["RunDiff"].mean()       # 0.0  -- runs are zero-sum across the league
   median = df["RunDiff"].median()   # about -13.5
   extremes = df.sort_values("RunDiff", ascending=False).iloc[[0, 1, -2, -1]]
   print(extremes[["Team", "W", "RS", "RA", "RunDiff"]].to_string())

   The extremes that pull the average

   mean run differential = 0.0, median = -13.5
   
            Team    W   RS   RA  RunDiff
   0      Braves  104  947  716      231
   2     Dodgers  100  906  699      207
   27    Rockies   59  721  957     -236
   29  Athletics   50  585  924     -339

   There they are. A small number of dominant teams — the Braves at +231, the Dodgers at +207 — drag the mean upward, while the bulk of the league sits just below zero. The cellar is even more extreme: the Athletics' −339 is a far longer tail than anything on the positive side. That asymmetry is exactly what "skew" means, and it's why the median is the more honest "typical" team here.

3. Draw the distribution

   A histogram buckets the values and counts how many fall in each bucket, turning the column into a shape. We'll mark the mean and median so the skew we just spotted is visible, not just asserted.

   import matplotlib.pyplot as plt
   
   fig, ax = plt.subplots(figsize=(8, 5))
   ax.hist(df["RunDiff"], bins=10, color="#5B6E5A", edgecolor="#FBF7EE")
   ax.axvline(mean, color="#B23A3A", label=f"mean ({mean:.0f})")
   ax.axvline(median, color="#2C5E8A", ls="--", label=f"median ({median:.0f})")
   ax.set_xlabel("run differential (runs scored - runs allowed)")
   ax.set_ylabel("number of teams")
   ax.legend()
   fig.savefig("rundiff_distribution.png", dpi=144, bbox_inches="tight")

   

   The picture confirms the numbers: a tall cluster near zero, a gentle right shoulder of strong teams, and a long left tail reaching out to the Athletics. The solid mean line and dashed median line sit just apart — a small visual gap that is the whole story of skew. The number of bins is a judgment call: too few hides the shape, too many turns it into noise. Ten is a sensible start for thirty teams.

Troubleshooting