Frequency-Weighted Median Estimator

You are given a compressed integer distribution in a table named Numbers:

• num: an integer value
• frequency: how many times that value appears in the full dataset

Each row represents many repeated observations of the same value.

Your task is to compute the median of the fully expanded dataset without explicitly materializing all repeated rows.

Output requirements:

• Return exactly one row with one column named median.
• Round the median to one decimal place.

Notes:

• Numbers.num values are unique.
• Median follows the standard statistical definition:
  • odd total count: middle value
  • even total count: average of the two middle values

This problem should be solved in both:

• SQL (SQLite 3.27.2)
• Pandas

Numbers:
| num | frequency |
|-----|-----------|
| 0   | 7         |
| 1   | 1         |
| 2   | 3         |
| 3   | 1         |

[
  {"median": 0.0}
]

Numbers:
| num | frequency |
|-----|-----------|
| 2   | 1         |
| 4   | 1         |
| 9   | 1         |
| 10  | 1         |

[
  {"median": 6.5}
]

Numbers:
| num | frequency |
|-----|-----------|
| -5  | 2         |
| -1  | 3         |
| 8   | 4         |

[
  {"median": -1.0}
]