Replace some means in Stats with medians (#3900)

* Display median interval in Stats instead of mean

Median is better suited than mean for reporting skewed data.

* Display median ease in Stats instead of mean

* Update difficulty.ts

* Update ease.ts

* Update statistics.ftl

* Format eases.rs

* Remove unused import

* Change Median back to Average in UI

* Revert "Change Median back to Average in UI"

This reverts commit e0c1e3f8e4.

* Preserve the old translations for now (dae)

ftl/core/statistics.ftl

@@ -148,7 +148,7 @@ statistics-card-ease-title = Card Ease
 statistics-card-difficulty-title = Card Difficulty
 statistics-card-stability-title = Card Stability
 statistics-card-stability-subtitle = The delay at which retrievability falls to 90%.
-statistics-average-stability = Average stability
+statistics-median-stability = Median stability
 statistics-card-retrievability-title = Card Retrievability
 statistics-card-ease-subtitle = The lower the ease, the more frequently a card will appear.
 statistics-card-difficulty-subtitle2 = The higher the difficulty, the slower stability will increase.
@@ -261,7 +261,7 @@ statistics-total = Total
 statistics-days-studied = Days studied
 statistics-average-answer-time-label = Average answer time
 statistics-average = Average
-statistics-average-interval = Average interval
+statistics-median-interval = Median interval
 statistics-due-tomorrow = Due tomorrow
 # This string, ‘Daily load,’ appears in the ‘Future due’ table and represents a
 # forecasted estimate of the number of cards expected to be reviewed daily in 
@@ -287,11 +287,19 @@ statistics-cards-per-day =
         [one] { $count } card/day
        *[other] { $count } cards/day
     }
-statistics-average-ease = Average ease
-statistics-average-difficulty = Average difficulty
+statistics-median-ease = Median ease
+statistics-median-difficulty = Median difficulty
 statistics-average-retrievability = Average retrievability
 statistics-estimated-total-knowledge = Estimated total knowledge
 statistics-save-pdf = Save PDF
 statistics-saved = Saved.
 statistics-stats = stats
 statistics-title = Statistics
+
+## These strings are no longer used - you do not need to translate them if they
+## are not already translated.
+
+statistics-average-stability = Average stability
+statistics-average-interval = Average interval
+statistics-average-ease = Average ease
+statistics-average-difficulty = Average difficulty

rslib/src/stats/graphs/eases.rs

@@ -10,37 +10,46 @@ impl GraphsContext {
     /// (SM-2, FSRS)
     pub(super) fn eases(&self) -> (Eases, Eases) {
         let mut eases = Eases::default();
-        let mut card_with_ease_count: usize = 0;
+        let mut ease_values = Vec::new();
         let mut difficulty = Eases::default();
-        let mut card_with_difficulty_count: usize = 0;
+        let mut difficulty_values = Vec::new();
         for card in &self.cards {
             if let Some(state) = card.memory_state {
                 *difficulty
                     .eases
                     .entry(percent_to_bin(state.difficulty() * 100.0))
                     .or_insert_with(Default::default) += 1;
-                difficulty.average += state.difficulty();
-                card_with_difficulty_count += 1;
+                difficulty_values.push(state.difficulty());
             } else if matches!(card.ctype, CardType::Review | CardType::Relearn) {
                 *eases
                     .eases
                     .entry((card.ease_factor / 10) as u32)
                     .or_insert_with(Default::default) += 1;
-                eases.average += card.ease_factor as f32;
-                card_with_ease_count += 1;
+                ease_values.push(card.ease_factor as f32);
             }
         }
-        if card_with_ease_count != 0 {
-            eases.average = eases.average / 10.0 / card_with_ease_count as f32;
-        }
-        if card_with_difficulty_count != 0 {
-            difficulty.average = difficulty.average * 100.0 / card_with_difficulty_count as f32;
-        }
+
+        eases.average = median(&mut ease_values) / 10.0;
+        difficulty.average = median(&mut difficulty_values) * 100.0;
 
         (eases, difficulty)
     }
 }
 
+/// Helper function to calculate the median of a vector
+fn median(data: &mut [f32]) -> f32 {
+    if data.is_empty() {
+        return 0.0;
+    }
+    data.sort_by(|a, b| a.partial_cmp(b).unwrap());
+    let mid = data.len() / 2;
+    if data.len() % 2 == 0 {
+        (data[mid - 1] + data[mid]) / 2.0
+    } else {
+        data[mid]
+    }
+}
+
 /// Bins the number into a bin of 0, 5, .. 95
 pub(super) fn percent_to_bin(x: f32) -> u32 {
     if x == 100.0 {

ts/routes/graphs/difficulty.ts

@@ -101,7 +101,7 @@ export function prepareData(
     const xTickFormat = (num: number): string => localizedNumber(num, 0) + "%";
     const tableData = [
         {
-            label: tr.statisticsAverageDifficulty(),
+            label: tr.statisticsMedianDifficulty(),
             value: xTickFormat(data.average),
         },
     ];

ts/routes/graphs/ease.ts

@@ -106,8 +106,8 @@ export function prepareData(
     const xTickFormat = (num: number): string => localizedNumber(num, 0) + "%";
     const tableData = [
         {
-            label: tr.statisticsAverageEase(),
-            value: xTickFormat(sum(Array.from(allEases.entries()).map(([k, v]) => (k + 2.5) * v)) / total),
+            label: tr.statisticsMedianEase(),
+            value: xTickFormat(data.average),
         },
     ];
 

ts/routes/graphs/intervals.ts

@@ -10,7 +10,7 @@ import * as tr from "@generated/ftl";
 import { localizedNumber } from "@tslib/i18n";
 import { timeSpan } from "@tslib/time";
 import type { Bin } from "d3";
-import { bin, extent, interpolateBlues, mean, quantile, scaleLinear, scaleSequential, sum } from "d3";
+import { bin, extent, interpolateBlues, quantile, scaleLinear, scaleSequential, sum } from "d3";
 
 import type { SearchDispatch, TableDatum } from "./graph-helpers";
 import { numericMap } from "./graph-helpers";
@@ -168,12 +168,12 @@ export function prepareIntervalData(
         dispatch("search", { query });
     }
 
-    const meanInterval = Math.round(mean(allIntervals) ?? 0);
-    const meanIntervalString = timeSpan(meanInterval * 86400, false);
+    const medianInterval = Math.round(quantile(allIntervals, 0.5) ?? 0);
+    const medianIntervalString = timeSpan(medianInterval * 86400, false);
     const tableData = [
         {
-            label: fsrs ? tr.statisticsAverageStability() : tr.statisticsAverageInterval(),
-            value: meanIntervalString,
+            label: fsrs ? tr.statisticsMedianStability() : tr.statisticsMedianInterval(),
+            value: medianIntervalString,
         },
     ];