This notebook continues the opening chapter with a small toy dataset.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
x = np.array([1.2, 0.7, 1.5, 2.1, 0.9, 1.8, 1.1, 1.4])
summary = pd.DataFrame({
"observation": np.arange(1, len(x) + 1),
"value": x,
})
summary| observation | value | |
|---|---|---|
| 0 | 1 | 1.2 |
| 1 | 2 | 0.7 |
| 2 | 3 | 1.5 |
| 3 | 4 | 2.1 |
| 4 | 5 | 0.9 |
| 5 | 6 | 1.8 |
| 6 | 7 | 1.1 |
| 7 | 8 | 1.4 |
n = len(x)
xbar = x.mean()
m2 = np.mean((x - xbar) ** 2)
m3 = np.mean((x - xbar) ** 3)
m4 = np.mean((x - xbar) ** 4)
pd.DataFrame({
"quantity": ["n", "xbar", "m2", "m3", "m4"],
"value": [n, xbar, m2, m3, m4],
})| quantity | value | |
|---|---|---|
| 0 | n | 8.000000 |
| 1 | xbar | 1.337500 |
| 2 | m2 | 0.187344 |
| 3 | m3 | 0.023496 |
| 4 | m4 | 0.073730 |
fig, ax = plt.subplots(figsize=(6.2, 4.0))
ax.hist(x, bins=5, color="#2f6c8f", edgecolor="white")
ax.axvline(xbar, color="#c44536", linestyle="--", linewidth=2)
ax.set_xlabel("Value")
ax.set_ylabel("Count")
ax.set_title("Toy sample")
plt.show()