EAL
GCSE Maths · Averages from grouped data
Before you watch

Where this fits
in engineering

Quoting a job means predicting labour hours. The welding bay tallies its work in time bands, so the detail is gone but the shape of the data survives.

Fillet weldA weld laid into the corner where two plates meet at an angle, triangular in section. The most common joint in fabrication.
Weld timeHow long an operator spends actually laying a weld, excluding set-up and repositioning.
Grouped dataRecords kept in bands rather than as individual values, which is normal where jobs are tallied rather than timed.
Welding bay, weekly log

Sixty
Welds

The supervisor tallied last week’s welds into ten-minute bands and threw the tally sheet away. Planning still needs an average time per weld to quote the next contract.

Welds recorded
60 jobs
Individual times kept
0 of them
You cannot find the mean. But you can get close enough to quote on.
Step 1
Step 2
Step 3

All you have is the grouped table

Assume every weld sat at the midpoint

Multiply, then total the column

22 welds took between 20 and 30 minutes. You do not know which minute. That information is gone.
Midpoint of 20 to 30 is 25. Add the ends and halve. Some welds were quicker, some slower, and it balances out.
Σfx = 1480. That is the estimated total welding time, in minutes.
Weld time t (min)Frequency f Midpoint x f × x
0 < t ≤ 106530
10 < t ≤ 201415210
20 < t ≤ 302225550
30 < t ≤ 401235420
40 < t ≤ 50645270
Totals60 1480

An estimate you can quote on

Estimated mean: divide by how many welds there were
1480 ÷ 60
= 24.666…
= 24.7 min
And Σfx was already the answer to a different question
1480 minutes
= 24 h 40 min
Nearly 25 hours of welding a week from 60 jobs.
Σfx is a labour budget, not just a stepping stone.

Three things to carry into the exam

  • Use midpoints, and call the answer an estimate, which is a marked point
  • Modal class here is 20 < t ≤ 30, and so is the class holding the median
  • Divide Σfx by Σf, never by the number of classes
A second bay logs 40 welds: 8 in 0–10, 18 in 10–20, 10 in 20–30 and 4 in 30–40. Estimate its mean weld time.
40 + 270 + 250 + 140 = 700
700 ÷ 40 = 17.5 min
0:00

The engineering

context and terms

Quoting a fabrication job means predicting labour hours, and labour is usually the largest single cost. The welding bay keeps records, but often as tallies in time bands rather than a stopwatch reading for every job. That is normal, and the detail is lost while the shape of the data survives. Estimating a mean from grouped data is how an estimator gets from a tally sheet to an hourly figure they can put in front of a customer.

Fillet weld
A weld laid into the corner where two plates meet at an angle, triangular in section. The most common joint in fabrication.
Weld time
How long an operator spends actually laying a weld, excluding set-up and repositioning.
Grouped data
Records kept in bands rather than as individual values, which is normal where jobs are tallied rather than timed.
Class interval
One of those bands, for example 20 to 30 minutes.
Estimating
Pricing a job before it is made, by predicting the hours and materials it will take.

Questions

4 questions · 11 marks
Write your answer, then check it.
  1. Write down the modal class. [1]
  2. Identify the class that contains the median weld time, and justify your answer. [2]
  3. Estimate the mean weld time. Give your answer to 1 decimal place. [3]
  4. A second welding bay logs 40 welds: 8 took 0–10 minutes, 18 took 10–20, 10 took 20–30 and 4 took 30–40. Estimate the mean weld time for the second bay and compare the two bays. [5]

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