ARCH-M1-11: Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-M1-11: Why the 135s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~135s (Blows 90s Clock)

Original total mass

= 18 \times 72 = 1296\text{ kg}

. New mean

= 72 + 1.5 = 73.5\text{ kg}

, so new total mass

= 20 \times 73.5 = 1470\text{ kg}

. The

2

new rowers have combined mass

1470 - 1296 = 174\text{ kg}

, giving a mean of

\frac{174}{2} = 87\text{ kg}

(~115s).

The Fast ShortcutTarget: 40s (Saves 95s)

Line 1 (Deviation Balance): New mean is

73.5\text{ kg}

; the

18

original rowers need

+1.5\text{ kg}

each (

+27\text{ kg}

total).
Line 2 (Split Surplus Across 2):

73.5 + \frac{27}{2} = 73.5 + 13.5 = 87\text{ kg}

(20s).

Where Students Lose Time: In 9 past UAT-UK questions (4% of Mathematics 1), candidates lose 95s by ignoring sample size weights when combining subgroup means. Instead, apply M6 with Maths 1 skill M6.5.

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