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UAT-UK SPEC: M6MODULE: MATHEMATICS 1TOPIC ID: ARCH-M1-11

Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms

Master Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms on the ESAT Mathematics 1 paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 40s, saving +95s per question.

Standard Classroom Time
135s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
40s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+95s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Deviation Balance): New mean is 73.5 kg73.5\text{ kg}; the 1818 original rowers need +1.5 kg+1.5\text{ kg} each (+27 kg+27\text{ kg} total).

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Split Surplus Across 2): 73.5+272=73.5+13.5=87 kg73.5 + \frac{27}{2} = 73.5 + 13.5 = 87\text{ kg} (20s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1subsystem_isolation_trap

Taking unweighted average (mean(A) + mean(B))/2 when group sizes n(A) != n(B)

Ignoring sample size weights when combining subgroup means.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2unit_or_prefix_mismatch

Reading histogram bar height (frequency density) as frequency without multiplying by class width

Confusing y-axis frequency density with raw count across unequal class intervals.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3fence_post_or_domain_trap

Using class midpoint instead of linear interpolation across the median class width

Assuming the median sits at the midpoint of the interval regardless of cumulative frequency position.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms

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Full Lesson All 15 Questions (ARCH-M1-11)
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ARCH-M1-11: Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms (Sample)Mathematics 1
00:00.0
SUB-90 ZONE (<55S)
0.0s55s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-M1-11 (6-Card Lesson)Format: Standard 5-Option
1-5Choose•FFlag•SScratchpad•EnterNext
Question 1 of 1 • 90s Target

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Mathematics 1•ARCH-M1-11•Standard 5-Option
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