# Plan: Add Median Statistic to Wakeup and Bedtime Plots

## Overview
The goal is to add a fourth statistic, "Median", to the summary section below the Wakeup and Bedtime trend graphs in `WakeupPlot.tsx` and `BedtimePlot.tsx`. Currently, these components display "Earliest", "Latest", and "Average".

## Detailed Tasks

### 1. Update `frontend/src/components/stats/WakeupPlot.tsx`
- **Sub-task 1.1: Update Statistics Calculation**
  - Locate the `stats` `useMemo` block.
  - Calculate the median of `validMinutes`. 
    - *Note*: To calculate the median, sort the array and pick the middle element (or average of two middle elements if even).
  - Include `median` in the returned object: `{ min, max, avg, median }`.
- **Sub-task 1.2: Update UI Layout**
  - Find the statistics container div (currently `grid grid-cols-3`).
  - Change the Tailwind class from `grid-cols-3` to `grid-cols-4`.
- **Sub-task 1.3: Add Median Display**
  - Add a new `div` for the "Median" statistic.
  - Use identical styling to the existing three blocks.
  - Display the value using `formatMinutesAfter(Math.round(stats.median), wakeup_ref)`.

### 2. Update `frontend/src/components/stats/BedtimePlot.tsx`
- **Sub-task 2.1: Update Statistics Calculation**
  - Locate the `stats` `useMemo` block.
  - Calculate the median of `validMinutes`.
  - Include `median` in the returned object: `{ min, max, avg, median }`.
- **Sub-task 2.2: Update UI Layout**
  - Find the statistics container div (currently `grid grid-cols-3`).
  - Change the Tailwind class from `grid-cols-3` to `grid-cols-4`.
- **Sub-task 2.3: Add Median Display**
  - Add a new `div` for the "Median" statistic.
  - Use identical styling to the existing three blocks.
  - Display the value using `formatMinutesAfter(Math.round(stats.median), bedtime_ref)`.

## Verification Plan
1. **Visual Inspection**: Ensure the four statistics are evenly spaced and aligned in a single row below each graph.
2. **Logic Check**: Manually verify with a small set of known numbers (e.g., [10, 20, 30] -> median 20; [10, 20, 30, 40] -> median 25) that the calculation is correct.