1.What this page explains
At C1, it is not enough merely to describe a graph. You need to structure, compare, contextualize, interpret, and qualify data.
Core distinction:
description
→ What is visible?
interpretation
→ What might it mean?
explanation
→ Which factors might be behind it?
evaluation
→ How robust and relevant is the claim?
Example:
Der Anteil steigt von 40 auf 50 Prozent.
That is description.
Das entspricht einem Anstieg um 10 Prozentpunkte beziehungsweise um 25 Prozent relativ zum Ausgangswert.
That is more precise quantitative interpretation.
Der Anstieg könnte auf eine veränderte Nachfrage hindeuten; aus dem Diagramm allein lässt sich jedoch keine Ursache ableiten.
That is interpretation with methodological caution.
At C1, several levels must therefore be controlled simultaneously:
chart type
source
time period
unit
denominator
absolute and relative values
distribution
trend
outliers
uncertainty
sample
correlation and causation
linguistic qualification
Core rule:
Data show patterns. Interpretation explains possible meaning. Causality requires additional evidence.
The page is reference and self-study material. It contains no exercises or tests.
2.1. Description, interpretation, explanation
These three levels should be kept linguistically distinct.
Examples:
Die Linie steigt. → Beschreibung
Das könnte auf höhere Nachfrage hindeuten. → Interpretation
3.2. Overview before detail
A strong C1 text starts with the overall pattern before moving to individual values.
Examples:
Insgesamt zeigt sich ein Aufwärtstrend.
4.3. Identify the chart type
Line, bar, column, pie, area, and scatter plots answer different kinds of questions.
Examples:
Das Liniendiagramm zeigt die Entwicklung über die Zeit.
5.4. Check the source
Source and data producer affect how robust and comparable the data are.
Examples:
Die Daten stammen von ...
6.5. Check the time period
A three-month trend must be interpreted differently from a ten-year trend.
Examples:
zwischen 2018 und 2025
7.6. Check the unit
Percentages, percentage points, euros, index values, counts, and rates are not interchangeable.
Examples:
in Prozent
in Tausend
Index 2020 = 100
8.7. Check the denominator
A proportion is meaningful only when its denominator is clear.
Examples:
Anteil der Befragten
Anteil am Gesamtumsatz
9.8. Absolute vs relative values
Absolute values show scale; relative values make differently sized groups easier to compare.
Examples:
500 Fälle ↔ 5 Prozent
10.9. Watch the scale
A truncated axis can visually exaggerate small differences.
Examples:
Die y-Achse beginnt nicht bei null.
11.10. Read axes and categories
Before interpretation, make sure the x- and y-axes are understood.
Examples:
x-Achse: Jahre; y-Achse: Umsatz in Mio. Euro
12.11. Do not overinterpret the title
A chart title can frame interpretation; the underlying values should still be examined independently.
Examples:
Titel ≠ Beweis
13.12. C1 goal
At C1, the goal is quantitative precision combined with methodological restraint.
Examples:
präzise beschreiben → vorsichtig interpretieren
14.13. Upward trend
A stable upward trend should be distinguished from a one-off jump.
Examples:
Die Werte steigen über mehrere Jahre kontinuierlich an.
15.14. Downward trend
For a decline, pace, duration, and starting level also matter.
Examples:
Die Zahl geht allmählich zurück.
16.15. Stagnation
Nearly constant values should not be interpreted as a trend when fluctuations are small.
Examples:
Die Werte bleiben weitgehend stabil.
17.16. Fluctuation
When data fluctuate strongly, the mean alone may be uninformative.
Examples:
Die Werte schwanken erheblich.
18.17. Break in trend
A change in direction can be more analytically important than the final value.
Examples:
Ab 2023 kehrt sich der Trend um.
19.18. Turning point
A turning point should be located precisely in time and then explained cautiously.
Examples:
Der Wendepunkt liegt im zweiten Quartal 2024.
20.19. Plateau
After strong growth, a plateau may indicate saturation, capacity limits, or simply temporary stabilization.
Examples:
Seit Mitte 2024 bewegt sich der Wert seitwärts.
21.20. Acceleration
Not only direction but also the rate of change can be relevant.
Examples:
Der Anstieg beschleunigt sich deutlich.
22.21. Deceleration
A positive trend can continue even while growth slows.
Examples:
Die Werte steigen weiter, jedoch weniger stark.
23.22. Volatility
High volatility means short-term values fluctuate strongly; it does not automatically imply a long-term trend.
Examples:
Kurzfristige Ausschläge dominieren das Bild.
24.23. Seasonal patterns
Recurring peaks and troughs may have seasonal causes.
Examples:
Im Sommer liegen die Werte regelmäßig höher.
25.24. Distinguish trend and cycle
A cyclical pattern may show recurring ups and downs despite a long-term trend.
Examples:
Langfristig steigt der Wert, kurzfristig verläuft er zyklisch.
26.25. Percent vs percentage points
An increase from 40% to 50% is 10 percentage points but 25% relative growth.
Examples:
40 % → 50 % = +10 Prozentpunkte = +25 % relativ
27.26. Calculate relative change
Relative change is measured relative to the starting value.
(neuer Wert - alter Wert) / alter Wert × 100
28.27. Base effect
A large relative increase can result from a very small starting value.
Examples:
1 → 2 = +100 %, aber absolut nur +1
29.28. Large absolute, small relative change
With large starting values, a large absolute increase may look small in percentage terms.
Examples:
1.000 → 1.050 = +50, aber nur +5 %
30.29. Shares and totals
A rising share does not necessarily mean a rising absolute count.
Examples:
Anteil steigt, obwohl Gesamtmenge sinkt.
31.30. Index values
An index shows change relative to a base year, not necessarily absolute quantities.
Examples:
Index 2020 = 100
32.31. Interpreting index 120
With a base of 100, an index of 120 typically means 20% above the base value.
Examples:
Index = 120
33.32. Watch for rebasing
When the base year changes, series are directly comparable only if methodology remains consistent.
Examples:
Basisjahr 2015 ≠ Basisjahr 2020
34.33. Rates
Rates relate events to a denominator, for example per 1,000 people.
Examples:
12 Fälle pro 1.000 Personen
35.34. Share vs rate
A share describes part of a whole; a rate may additionally include time or exposure.
Examples:
5 % Anteil ≠ 5 pro 1.000 pro Jahr
36.35. Cumulative values
Cumulative series often rise mechanically because values are accumulated.
Examples:
kumulierte Zahl
37.36. Average growth rate
An average growth rate can hide fluctuations within the period.
Examples:
im Durchschnitt jährlich um 4 %
38.37. Mean
The mean is sensitive to extreme values.
Examples:
Durchschnitt = Summe / Anzahl
39.38. Median
The median divides an ordered distribution in half and is more robust to outliers.
Examples:
Median statt Mittelwert bei stark schiefer Verteilung
40.39. Mean vs median
A large gap between them may indicate skewness or outliers.
Examples:
Mittelwert deutlich höher als Median
41.40. Range
The range shows the distance between minimum and maximum but little about values in between.
Examples:
Maximum - Minimum
42.41. Quartiles
Quartiles help describe the middle 50% of a distribution.
Examples:
25. Perzentil · Median · 75. Perzentil
43.42. Outliers
Outliers can be measurement errors, special cases, or genuine extreme observations.
Examples:
Ein einzelner Wert liegt weit außerhalb des Musters.
44.43. Do not automatically remove outliers
Before removing an outlier, determine why it is extreme.
Examples:
Ausreißer ≠ automatisch Fehler
45.44. Skewed distribution
For skewed distributions, the median often represents the typical value better than the mean.
Examples:
Einkommen sind häufig rechtsschief verteilt.
46.45. Multimodal distribution
Several peaks can indicate different subgroups.
Examples:
zwei deutliche Häufungen
47.46. Dispersion
Two groups can have the same mean but very different dispersion.
Examples:
gleicher Durchschnitt, unterschiedliche Variabilität
48.47. Standard deviation
Standard deviation describes how strongly values typically vary around the mean.
Examples:
kleine vs. große Standardabweichung
49.48. Distribution before summary
A single summary statistic should never automatically stand in for the full distribution.
Examples:
Mittelwert allein reicht oft nicht.
50.49. Group averages can mislead
Different group sizes or compositions can create apparent effects.
Examples:
Zusammensetzung der Gruppen prüfen.
51.50. Aggregated and disaggregated data
An overall trend may look different within subgroups.
Examples:
Gesamtwert vs. Altersgruppen
52.51. Direct comparison
When comparing groups, time period, unit, and denominator should match.
Examples:
Gruppe A liegt über Gruppe B.
53.52. Ranking
A ranking shows positions but not automatically large or meaningful differences.
Examples:
Platz 1 und Platz 2 können fast gleichauf liegen.
54.53. Gap
A gap should be quantified in absolute or relative terms.
Examples:
Der Abstand beträgt 8 Prozentpunkte.
55.54. Convergence
When two series converge, this can result from one rising, the other falling, or both.
Examples:
Die Differenz verringert sich.
56.55. Divergence
A widening gap should be interpreted in relation to cause and starting level.
Examples:
Die beiden Reihen entwickeln sich zunehmend auseinander.
57.56. Crossing series
A crossing marks a relative rank change, not automatically a structural break.
Examples:
Ab 2024 liegt A über B.
58.57. Normalization
Normalized values make differently scaled quantities easier to compare.
Examples:
je Einwohner
pro Beschäftigten
59.58. Per-capita values
Per-capita values help comparison but can hide within-group distribution.
Examples:
Umsatz pro Beschäftigten
60.59. Logarithmic scale
On logarithmic axes, equal distances represent equal relative rather than absolute changes.
Examples:
10 → 100 → 1000
61.60. Stacked bars
Stacked charts show total and composition but make internal segment comparison harder.
Examples:
Anteil einzelner Kategorien
62.61. Read pie charts critically
Pie charts suit part-to-whole relationships, but small angular differences are difficult to compare.
Examples:
Balken sind für feine Vergleiche oft besser.
63.62. Scatter plot
Scatter plots show relationships between two numerical variables.
Examples:
x: Arbeitszeit; y: Output
64.63. Trend line
A trend line summarizes a pattern but should not hide dispersion and exceptions.
Examples:
Die Punkte streuen stark um die Linie.
65.64. Visual weighting
Color, size, and ordering can steer attention without adding new data.
Examples:
Darstellung beeinflusst Wahrnehmung.
66.65. Sample size
Small samples lead to greater uncertainty and less stable estimates.
Examples:
n = 30 vs. n = 3.000
67.66. Representativeness
A large sample is not automatically representative if selection is biased.
Examples:
Selbstselektion kann Ergebnisse verzerren.
68.67. Confidence interval
A confidence interval shows a range of uncertainty around an estimate.
Examples:
Schätzwert 52 %, Intervall 49–55 %
69.68. Overlapping intervals
Overlapping confidence intervals do not automatically imply equality; significance requires appropriate tests.
Examples:
visuelle Überlappung ≠ endgültiger Signifikanztest
70.69. Missing values
Missing data may be random or systematic and can change interpretation.
Examples:
fehlende Angaben prüfen
71.70. Measurement error
Measurement methods can introduce systematic or random error.
Examples:
Messgenauigkeit berücksichtigen
72.71. Definitions can change
Time series become hard to compare when categories or collection methods change.
Examples:
Methodenbruch im Jahr 2022
73.72. Revisions
Preliminary data may later be revised.
Examples:
vorläufige Werte
74.73. Rounding
Rounded values can create apparent equalities or small differences.
Examples:
49,6 % → 50 %
75.74. Missing value vs zero
A missing value is not the same as zero.
Examples:
keine Angabe ≠ 0
76.75. Mark uncertainty linguistically
With uncertain data, phrases such as deutet darauf hin, scheint, and dürfte are more appropriate than absolute statements.
Examples:
Die Daten deuten auf einen leichten Anstieg hin.
77.76. Do not overstate uncertainty
Methodological caution should increase precision, not make every claim vague.
Examples:
starke Daten erlauben stärkere Formulierungen
78.77. Correlation
Correlation describes a statistical relationship between variables.
Examples:
Mit höherem X steigt häufig Y.
79.78. Correlation ≠ causation
An association alone does not prove that X causes Y.
Examples:
Zusammenhang ist kein Ursachenbeweis.
80.79. Confounding variable
A third variable may influence both X and Y.
Examples:
Alter könnte beide Variablen beeinflussen.
81.80. Reverse causality
Sometimes X does not cause Y; instead Y influences X.
Examples:
Richtung der Wirkung prüfen.
82.81. Spurious correlation
Two variables can rise together without being meaningfully related.
Examples:
gemeinsamer Zeittrend kann täuschen
83.82. Temporal order
For causality, the proposed cause must precede the effect in time.
Examples:
Ursache vor Wirkung
84.83. Plausible mechanism
A causal interpretation is stronger when a plausible mechanism is known.
Examples:
Wie genau könnte X auf Y wirken?
85.84. Alternative explanations
A good interpretation mentions several plausible explanations when the data do not identify one cause.
Examples:
Neben Preis könnten Verfügbarkeit und Saison eine Rolle spielen.
86.85. Experimental evidence
Controlled experiments can support causal inference more strongly than observational data alone.
Examples:
randomisierte Zuweisung
87.86. Observational data
With observational data, causal wording should be especially cautious.
Examples:
steht in Zusammenhang mit
88.87. Grade causal language
There are several linguistic levels between association and causation.
steht in Zusammenhang mit
geht einher mit
könnte dazu beitragen
begünstigt möglicherweise
verursacht – nur bei starker Evidenz
89.88. Interpretation remains testable
A good explanation should be formulated so that additional data could support or refute it.
Examples:
Diese Hypothese ließe sich mit weiteren Daten prüfen.
90.89. Introducing a data interpretation
A good introduction briefly states chart type, topic, period, unit, and source.
Examples:
Das Diagramm zeigt ... im Zeitraum von ...
91.90. Overview sentence
The overview states the main overall pattern without flooding the reader with detail.
Examples:
Insgesamt zeigt sich ein deutlicher Anstieg mit anschließender Stabilisierung.
92.91. Prioritize details
Not every value is equally important. Selection should be analytically justified.
Examples:
Höchstwert, Tiefstwert, Wendepunkt, größte Differenz
93.92. Vary comparative language
Advanced texts avoid monotonous repetition of higher and lower.
Examples:
liegt über
übertrifft
bleibt hinter
nähert sich an
94.93. Qualify interpretation
Interpretive claims should be phrased according to evidential strength.
Examples:
könnte darauf hindeuten
spricht dafür
lässt vermuten
95.94. Separate description and evaluation
A high value is not automatically good or bad; evaluation requires a criterion.
Examples:
hoch ≠ positiv
96.95. Conclusion section
A good conclusion summarizes pattern, uncertainty, and key interpretation without adding new data.
Examples:
Zusammenfassend lässt sich feststellen, dass ...
97.96. What to remember
Advanced data interpretation combines quantitative precision, methodological checking, and linguistic restraint.
zuerst Quelle, Zeitraum, Einheit und Bezugsgröße prüfen
absolute und relative Veränderungen unterscheiden
Prozent ≠ Prozentpunkte
Mittelwert ≠ Median
Verteilung und Ausreißer beachten
Skala und Darstellungsweise kritisch lesen
Unsicherheit und Stichprobe berücksichtigen
Korrelation ≠ Kausalität
Beschreibung ≠ Interpretation ≠ Erklärung
Schlussfolgerung nur so stark formulieren, wie die Daten erlauben
98.Summary
A useful C1 analysis path is:
1. identify the chart type
2. check source, period, and unit
3. clarify the denominator
4. describe the overall trend
5. select salient values and turning points
6. distinguish absolute and relative change
7. inspect distribution, dispersion, and outliers
8. account for uncertainty and sample
9. do not confuse correlation with causation
10. qualify interpretation linguistically
Important quantitative distinctions:
40 % → 50 %
= +10 percentage points
= +25 % relative change
mean
→ sensitive to outliers
median
→ more robust in skewed distributions
index 120 with base 100
→ 20 % above the base value
Useful language:
Insgesamt zeigt sich ...
Auffällig ist ...
Der Wert liegt deutlich über ...
Die Differenz beträgt ...
Ab ... kehrt sich der Trend um.
Die Daten deuten darauf hin, dass ...
Dies könnte damit zusammenhängen, dass ...
Aus dem Diagramm allein lässt sich jedoch nicht schließen, dass ...
At C1, data interpretation means calculating precisely, reading critically, and interpreting only as far as the evidence allows.