Ranked by One Metric, Scored by Another

A streaming service recommends shows by finding the single most similar user to you and copying what that user watched.

Each user is described by four features. Here is the query user $Q$ and the three candidate neighbours:

User	$f_1$ : ratings per week	$f_2$ : distinct genres	$f_3$ : minutes watched per day	$f_4$ : sessions per week
Q (query)	10	5	40	20
A	12	6	45	40
B	16	2	55	8
C	2	7	30	24

The four features are measured in wildly different units, so before any distance is computed each coordinate is divided by that feature's typical spread:

Feature	Typical spread $s_j$
$f_1$	2
$f_2$	1
$f_3$	5
$f_4$	4

So every user vector $v$ becomes $\tilde{v}$ with $\tilde{v}_j = v_j / s_j$ , and all distances below are measured on the scaled vectors.

The system does two different things with two different norms:

Retrieval. The index ranks the candidates by Manhattan ( $L_1$ ) distance from the query — it is far cheaper to compute at scale — and returns the single closest candidate.
Scoring. The number shown next to the recommendation is that returned neighbour's Euclidean ( $L_2$ ) distance from the query.

What number does the system display?

Give your answer rounded to two decimal places — for example 1.23.

Ranked by One Metric, Scored by Another

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