The client has two business lines. The core line is 70 percent of revenue at a 40 percent margin. The newer line is 30 percent of revenue at a 20 percent margin. The interviewer asks, "What is the blended margin?" Many candidates freeze, reach for long multiplication, or worse, just average 40 and 20 and say 30. The strongest candidates calculate it in one breath with a simple trick: anchor on the big number, then adjust.

Weighted averages show up everywhere in cases: blended margins, average price across channels, mix shift questions, and portfolio returns. Getting them fast and right, out loud, is a quiet signal that you are comfortable with numbers.

Why weighted averages trip people up

• Taking a simple average. 40 and 20 average to 30, but the 40 percent line is more than twice as big, so the true answer sits well above 30.
• Multiplying everything out. 0.7 times 40 plus 0.3 times 20 works, but under pressure it invites slips and silence.
• Weighting by the wrong thing. A margin is profit over revenue, so it must be weighted by revenue, not by units or customer count.

The anchor and adjust method

Say this out loud first: "I will anchor on the biggest segment, then adjust for how far the others sit from it, weighted by their share."

1) Pick the anchor

"The core line is 70 percent of revenue at 40 percent margin, so I will start at 40."

2) Find each gap

"The newer line is 20 points below the anchor."

3) Weight the gap

"It is 30 percent of revenue, so 30 percent of a 20 point gap is 6 points."

4) Adjust and sanity check

"40 minus 6 is a 34 percent blended margin. That sits between 20 and 40 and closer to 40, which makes sense because the core line is bigger." The sanity check takes two seconds and catches most mistakes.

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It scales to three segments

Segments at 50, 30, and 20 percent of revenue with margins of 30, 20, and 50 percent. Anchor at 30. The 20 percent margin segment is 10 points below with a 30 percent weight, so minus 3. The 50 percent margin segment is 20 points above with a 20 percent weight, so plus 4. Net plus 1, so the blend is 31 percent. Two small multiplications instead of three big ones.

Turn it into a so-what: mix shift

The same math answers the follow-up interviewers love: "What happens if the mix shifts?" If 10 more points of revenue move to the newer line, the blend drops by 10 percent of the 20 point gap, which is 2 points, from 34 to 32 percent. Say the so-what right after: "So growing the newer line faster than the core quietly erodes margin, even if neither line changes on its own." That is the insight the interviewer is looking for.

Common mistakes to avoid

• Averaging percentages with no weights at all.
• Weighting a per-revenue metric by units. Always weight by the denominator of the ratio.
• Skipping the sanity check. The blend must land between the lowest and highest values, closer to the heavier one.

10-minute drill

Write down five two or three segment setups with revenue shares and margins. For each one, give yourself 30 seconds, out loud: name the anchor, state each gap, weight it, adjust, and sanity check. Then add one mix shift question and say the so-what. Record yourself and count every time you multiply everything out or skip the sanity check. Repeat until both counts are zero.

A blended number is only as good as its weights. Anchor, adjust, and check, and you will calculate it faster than the interviewer can write it down.

Ready to practice? Start free case drills at CaseCrunchAI with timed cases, calculate practice, and feedback on how you say it.