Find Median Given Frequency of Numbers - Problem
You are given a table Numbers with the following structure:
num: The actual number (primary key)frequency: How many times this number appears
The median is the value separating the higher half from the lower half of a data sample. When we "decompress" the table by repeating each number according to its frequency, we need to find the median of all these numbers.
Write a SQL solution to find the median of all numbers after decompressing the table. Round the result to one decimal place.
Table Schema
Numbers
| Column Name | Type | Description |
|---|---|---|
num
PK
|
int | The actual number value (primary key) |
frequency
|
int | How many times this number appears |
Primary Key: num
Note: Each row shows a unique number and its frequency in the dataset
Input & Output
Example 1 — Basic Median Calculation
Input Table:
| num | frequency |
|---|---|
| 0 | 7 |
| 1 | 1 |
| 2 | 3 |
Output:
| median |
|---|
| 0 |
💡 Note:
After decompressing: [0,0,0,0,0,0,0,1,2,2,2] (11 numbers total). The median is the 6th number when sorted, which is 0. Result: 0.0
Example 2 — Even Count Median
Input Table:
| num | frequency |
|---|---|
| 1 | 2 |
| 2 | 2 |
Output:
| median |
|---|
| 1.5 |
💡 Note:
After decompressing: [1,1,2,2] (4 numbers total). The median is the average of 2nd and 3rd numbers: (1+2)/2 = 1.5
Example 3 — Single Number Multiple Times
Input Table:
| num | frequency |
|---|---|
| 5 | 10 |
Output:
| median |
|---|
| 5 |
💡 Note:
All 10 numbers are 5. The median of [5,5,5,5,5,5,5,5,5,5] is clearly 5.0
Constraints
-
1 ≤ Numbers.num ≤ 500 -
1 ≤ Numbers.frequency ≤ 10^4 -
The total frequency is guaranteed to be at least 1 -
Round the median to one decimal place
Visualization
Tap to expand
Understanding the Visualization
1
Input
Numbers table with frequency counts
2
Cumulate
Calculate running frequency totals
3
Locate
Find median position and return result
Key Takeaway
🎯 Key Insight: Use cumulative frequencies to find median position without expanding compressed data
💡
Explanation
AI Ready
💡 Suggestion
Tab
to accept
Esc
to dismiss
// Output will appear here after running code