Scientific Graphing Studio

Experimental Measurement, Reasoning & Mathematical Modelling Laboratory · v7.0

Workspace

▦Data & Setup4

∑Analyze8

⌬Measurement & Reasoning2

✦Graph Design3

⌁Teaching4

↺Project History1

Project & graph

Graph title

Mode

X-axis

Y-axis

X unit

Y unit

Scientific markup is supported in graph titles and axis text: T^2, 10^{-3}, E_a, mol dm^-3. Greek/scientific commands also work: \lambda, \Delta H, \mu, \sigma, \theta, \pm, \times. Plain unit exponents such as cm^3 and mol dm^-3 are formatted automatically.

Series

Active series data

#	x	y	±x	±y	Use

Paste data

Accepts tabs, commas, semicolons, or whitespace. Columns 3 and 4 become ±x and ±y.

Spreadsheet Clipboard Importer

Copy a rectangular range from Excel, Google Sheets, LibreOffice Calc or another spreadsheet and paste it here. V5 can map named columns instead of requiring a fixed order.

Raw-data provenance

No raw snapshot stored for this series yet.

Series management

Calculated series

Preset transformation

Quantity-Aware Formula Builder

Build a derived X–Y series from the active data. SGS propagates physical dimensions and SI units through the expression and checks any unit you enter.

X quantity type

Y quantity type

X source unit

Y source unit

Variables: x = active X quantity, y = active Y quantity. Functions: sqrt(), ln(), log10(), exp(), sin(), cos(), tan(), abs(). Operators: + − * / ^ and parentheses.

Derived X name

Derived X expression

Derived Y name

Derived Y expression

Expected X unit (optional)

Expected Y unit (optional)

Formula analysis will appear here.

Data cleaning

Moving average uses a 3-point centered window. Rounding asks for decimal places.

Scaling

X scale

Y scale

X divisions

Y divisions

X min

X max

Y min

Y max

X axis type

Y axis type

Display

Major grid Minor graph-paper grid Automatic scientific notation Show uncertainty bars

X uncertainty bars Y uncertainty bars End caps

Cap size / px

Line width / px

Line style

Error-bar color

Opacity

X and Y error bars can be shown independently. End caps are drawn at the ± uncertainty limits.

Show selected fit 95% confidence band (linear fit)

Physical Quantity & Unit Engine

V6 treats common scientific units as quantities with dimensions rather than only as axis-label text.

Quantity

Unit

Value

Convert to

Choose a quantity and unit.

Dimensional Analysis

Numerator quantity

Denominator quantity

No dimensional calculation yet.

Axis Quantity Awareness

Fit or measure a gradient first.

Interactive graph tools

Active tool

Selected points: 0. Ctrl-click is not required; choose Select points and click measurements to toggle them.

Gradient: click two data points. Tangent: click near the fitted curve. Intersection: click four boundary points on the active series: Region 1 start, Region 1 end, Region 2 start, Region 2 end. All measured points between each pair are used for a least-squares best-fit line. Drag-select can also fit a whole x-region. Auto two-line fit searches for the breakpoint that minimizes combined line-fit error.

Bidirectional Read-Off Tool

Project a known x or y value to the fitted curve or measured data, then read the corresponding coordinate from the other axis.

Direction

Known y value

Reference

Label

Horizontal guide Vertical guide Intersection marker Coordinate label

No read-off has been created yet.

Saved read-offs

Tool result

No active measurement.

Object & Style Inspector

Object

Marker

Marker size

Line width

Line style

Opacity

Connect points

Legend

Show legend

The legend is also draggable directly on the graph. Click a legend row to show/hide that series.

Regression uncertainty

Fit a linear dataset to estimate slope/intercept uncertainty.

Maximum / minimum gradient

Uses the first and last measured points and their y-error bars to estimate steepest and shallowest endpoint-consistent gradients. This is designed as a transparent school-laboratory uncertainty aid, not a substitute for a full statistical model.

No gradient bounds calculated.

Transform uncertainty propagation

Preset transforms still propagate uncertainty using first-order derivative rules. SGS V7 also adds a general formula-based RSS propagation engine in Measurement & Reasoning → Measurement laboratory.

SGS V7

Experimental Measurement Laboratory

Turn raw measurements into defensible experimental results using uncertainty, replicates, residuals, dimensional reasoning and comparison with theory.

Measurement → Evidence

1. Replicate Measurements Manager

If the active series contains repeated measurements at the same (or nearly the same) x value, SGS can summarize each group and create a new series containing the mean response and a statistically derived y uncertainty.

X grouping tolerance

Y uncertainty from replicates

No replicate analysis yet.

2. General Uncertainty Propagation

First-order propagation by root-sum-of-squares: u(f)² = (∂f/∂x·uₓ)² + (∂f/∂y·uᵧ)². It uses each row's ±x and ±y values and the same offline formula syntax as the Quantity-Aware Formula Builder.

Derived quantity name

Formula f(x,y)

Output unit

Independent variable for new series

Enter a formula and preview the propagated uncertainty.

3. Best / Worst Acceptable Gradient

V7 can use all available vertical error bars, not only the first and last point. It searches for the steepest and shallowest straight lines that can pass through every y-uncertainty interval.

Use all y-error bars Draw bounds on graph

No V7 gradient bounds calculated.

4. Residual Diagnostics

SGS checks for long sign runs, correlation with x, serial correlation, curvature and changing residual magnitude. These are diagnostic clues, not automatic proof that a model is wrong.

Fit a model first, then run residual diagnostics.

5. Theory vs Experiment

Experimental result

Experimental value

Experimental uncertainty ±

Accepted / theoretical value

Accepted uncertainty ±

Quantity / constant name

No comparison yet.

6. Gradient & Intercept Meaning

Fit a straight-line model or select an investigation module.

7. Experimental Quality Dashboard

The dashboard does not hide its scoring logic. Each component is shown separately so students can see what strengthened or weakened the evidence.

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SGS V7

Experimental Reasoning Workspace

A guided route from variables and measurements to model choice, physical meaning, evaluation and scientific conclusion.

Evidence → Reasoning → Conclusion

Workspace audience

Teacher reveal level

Run the reasoning workspace to build the evidence trail.

Scientific conclusion builder

SGS proposes a structured conclusion from the current evidence. Students should edit it so the wording reflects their own experiment and limitations.

Scientific Investigation Wizard

Subject

Module

Experiment Data Source

The selected investigation can analyze simulated measurements or your own experimental data. All routes use the same module analysis tools.

No user dataset has been checked against this module yet.

Generate Experimental Data

The controls below follow the selected Chemistry/Physics investigation. SGS generates imperfect classroom-style measurements, loads them into the active series, and plots them immediately.

Measurement realism

Number of readings

Random noise / %

X resolution

Y resolution

Systematic y offset

Reported ±x uncertainty

Reported ±y uncertainty

Anomalous readings

Missing readings

Random seed

Choose an investigation module. Its generator parameters will appear here.

Graph Presentation

Custom graph title

Analysis label appearance

Font size / px

Text color

Background

Border color

Drag an auto-generated label directly on the graph to reposition it. Double-click a label to change its text.

Analyze This Experiment

Choose an investigation module to see its recommended analysis workflow.

No module-specific analysis has been run yet.

Scientific Interpretation

Select an investigation module and run the analysis.

Enhanced Breakpoint Analysis

For two-region investigations such as thermometric and conductometric titrations.

No breakpoint landscape calculated.

Split	x	SSE	Intersection x

Equation Plotter & Parameter Sandbox

Function y =

x min

x max

Move a slider to see the theoretical curve change. The curve is stored as a special series and can be compared with measured data.

Graph annotations

Annotation tool

Annotations

No annotations yet.

Relationship Investigator

Use this when you have plotted an unfamiliar dataset but do not yet know whether the relationship is linear, inverse, inverse-square, square-root, inverse-square-root, exponential, power-law, logarithmic, quadratic, or saturation-type.

Evidence mode

Maximum candidates to show

No relationship investigation has been run yet.

Candidate Ranking

Run the investigator to compare candidate relationships.

Recommended Linearisation

No recommendation yet.

Linearisation Laboratory

SGS tests straight-line forms directly and ranks them independently of the nonlinear model fits.

No linearisation ranking yet.

Interpretation

No interpretation available yet.

Model Explorer

Model

Residuals

Show residual plot panel

The app reports R², adjusted R², RMSE and MAE. Model ranking penalizes extra parameters.

Advanced analysis

No advanced calculation yet.

Graph quality checker

No quality check run yet.

Uncertainty summary

No uncertainty analysis yet.

Custom Model Builder

Use x and parameters a, b, c, d. Supported functions: exp, log, ln, sqrt, sin, cos, tan, abs, pow.

Equation for y

a initial

b initial

c initial

d initial

No custom fit yet.

Linearisation Laboratory

Transformation

Choose a transformation to compare the original and transformed data.

Multi-Graph Workspace

Secondary graph

The workspace updates automatically when you change the derived view.

No relationship result available.

Choose a derived view above. The left graph shows the active measured series; the right graph shows the selected derived representation.

Teacher data generator

Relationship

A / a

k / n / b

x start

x end

Points

Random noise %

Systematic offset

Instrument resolution

Add anomalous point(s)

Outlier count

Missing point count

Correlated/drifting noise

Student / Teacher workflow

TEACHER

Switch mode in Data → Project & graph.

Exercise prompt

Expected numeric answer (optional)

Tolerance ±

Student answer

No answer checked yet.

Scale Challenge

Your x min

Your x max

Your x step

Your y min

Your y max

Your y step

No scale checked yet.

Teacher Activity Builder

Activity title Instructions

Student tool restrictions

Disable automatic model analysis Disable automatic-scale reset Disable automatic two-line fit Disable derivative/integral generation

Configure the activity, then apply the settings. Restrictions are enforced in Student mode.

Manual plotting challenge

Target x

Target y

Tolerance (% of plot span)

No plotting challenge active.

Manual best-fit challenge

Click two locations to draw your proposed straight line. V5 compares its gradient with least-squares regression for the active series.

No manual line submitted.

Experiment templates

My local templates

Template name

Templates are stored locally in this browser and remain fully offline.

Productivity

Ctrl+S save project Ctrl+Z undo Ctrl+Y redo Ctrl+P print

Analysis history

No recorded actions.

Processing pipeline

No processing steps recorded.

Local recovery snapshots

No snapshots yet.

Experimental Data

Ready

x: —, y: —

Multi-Graph Workspace

Measured data

Derived view

Residual plot

Data & model diagnostics

Scientific Meaning

Gradient interpretation

—

Intercept interpretation

—

Analysis summary

Model comparison

Run analysis on the active series.

Scientific Graphing Studio

Activity

Multi-Graph Workspace

Measured data

Derived view

Residual plot

Data & model diagnostics

Scientific Meaning

Analysis summary

Model comparison

Linearisation comparison

Original data

Transformed data

Scale Inspector