EAL
GCSE Maths · Scatter graphs and correlation
Before you watch

Where this fits
in engineering

Cut faster and the job finishes sooner, but the tool dies sooner too. A setter is balancing machine time against tooling cost with every speed they choose.

CNCComputer Numerical Control. The machine follows a programmed toolpath rather than being driven by hand.
Carbide insertA small replaceable cutting tip clamped into a tool holder. When the edge wears, the insert is indexed or swapped rather than the whole tool.
Cutting speedHow fast the workpiece surface passes the cutting edge, measured in metres per minute.
CNC section, tooling store

Tool
Life

A carbide insert costs Ashfield £34. Run the spindle harder and the job finishes sooner, but the tool dies sooner too. The section logged ten tools to find out how much sooner.

Recorded for each tool
2 values
Cutting speed, tool life
10 tools
Two numbers per tool. What can a graph tell you that a list cannot?
Step 1
Step 2
Step 3
Step 4

Plot one point per tool

Read the shape of the cloud

Draw the line of best fit

Use it carefully

One tool, one dot. Never join the dots up.
The red tool ran slowly and lasted well. That is the pattern, not an exception.
As speed rises, tool life falls. That is strong negative correlation.
Gradient = −62 ÷ 120 = −0.52
Every extra 1 m/min costs about half a minute of tool life.
At 400 m/min the line predicts a negative tool life. Outside the data, the line is a guess.
100 120 140 160 180 200 220 240 260 0 20 40 60 80 100 Cutting speed (m/min) Tool life (min) 165 m/min, 92 min 120 → 240 m/min 95 → 33 min 190 m/min → about 59 minutes

Three things to carry into the exam

  • Describe correlation by direction and strength, never by cause
  • The line of best fit splits the points, roughly half above and half below
  • Reading inside the data is safe; reading outside it is not
Use the line to estimate the tool life at a cutting speed of 130 m/min.
95 − 0.52 × 10
≈ 90 minutes
0:00

The engineering

context and terms

Every cut a CNC lathe makes wears the cutting edge away. Run the spindle faster and the job is off the machine sooner, but the insert is scrapped sooner too. A setter is balancing machine time against tooling cost every time they choose a speed. Plotting the two quantities against each other is how that trade-off becomes visible, and once there is a line through the points, predictable.

CNC
Computer Numerical Control. The machine follows a programmed toolpath rather than being driven by hand.
Carbide insert
A small replaceable cutting tip clamped into a tool holder. When the edge wears, the insert is indexed or swapped rather than the whole tool.
Cutting speed
How fast the workpiece surface passes the cutting edge, measured in metres per minute.
Tool life
How long an edge keeps cutting to specification before it has to be changed, measured here in minutes.
Bivariate data
Data where two values are recorded for the same item, which is what a scatter graph needs.

Questions

4 questions · 11 marks
Write your answer, then check it.
  1. Describe the correlation shown by the scatter graph. [2]
  2. Find the gradient of the line of best fit and explain what it means in this context. [3]
  3. Estimate the tool life at a cutting speed of 190 m/min. State whether this is interpolation or extrapolation. [2]
  4. A planner wants to use the line to predict the tool life at 400 m/min, and says the graph proves that fast cutting causes tool wear. Give two reasons the prediction is unsafe, and comment on the claim about cause. [4]

Controls. Tap the stage or press space to play and pause. Drag the amber circle along the line to scrub, or use the arrow keys to jump five seconds. The chapter buttons drop you straight into each stage of the working, which is the bit worth pausing on with a class. Captions start off; CC turns them on. Everything is inside this one file, so it runs offline. Screen-record the stage at 1920×1080 if you need an MP4 with a voiceover.

Demo developed by Lee Guthrie for EAL