Mathematics · Statistics
Mean Reciprocal Rank evaluated query count Solver
Rearrange the mean reciprocal rank relationship and solve for evaluated query count.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use b=a/c with mean reciprocal rank=0.64 and sum of first-relevant reciprocal ranks=64.
- evaluated query count=100.
- Substitution into c=a/b reconstructs 0.64.
Understand Mean Reciprocal Rank: solve evaluated query count
One idea, three depths
Choose how deeply to explain Mean Reciprocal Rank: solve evaluated query count
Mean Reciprocal Rank: solve evaluated query count: Rearrange the mean reciprocal rank relationship and solve for evaluated query count.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Mean Reciprocal Rank: solve evaluated query count to answer this question: rearrange the mean reciprocal rank relationship and solve for evaluated query count? Enter mean reciprocal rank and sum of first-relevant reciprocal ranks; the calculator shows evaluated query count. For example: sum of first-relevant reciprocal ranks=64 and evaluated query count=100 produce mean reciprocal rank=0.64. The answer tells you evaluated query count.
Age 15Explain it to a 15-year-oldConnect it to the formula
Mean reciprocal rank averages one divided by the rank of each query's first relevant result. This page isolates evaluated query count and verifies it in the original relationship. The rule is b=a/c. Its input values are mean reciprocal rank, sum of first-relevant reciprocal ranks, and the main result is evaluated query count. For example: sum of first-relevant reciprocal ranks=64 and evaluated query count=100 produce mean reciprocal rank=0.64.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated mean reciprocal rank: solve evaluated query count relation over the valid real-number domain stated below. The implemented relation is b=a/c, evaluated from mean reciprocal rank, sum of first-relevant reciprocal ranks to produce evaluated query count. Mean reciprocal rank averages one divided by the rank of each query's first relevant result. This page isolates evaluated query count and verifies it in the original relationship. It ignores relevant results appearing after the first.
Inputs and valid domain
- mean reciprocal rank must be a finite real number.
- sum of first-relevant reciprocal ranks must be a finite real number.
Important boundary: It ignores relevant results appearing after the first.
The formula
b=a/c
How the calculator works through it
It substitutes mean reciprocal rank, sum of first-relevant reciprocal ranks into the formula and exposes every numerical step above. The main output is evaluated query count, accompanied by Reconstructed mean reciprocal rank.
Read the result correctly
The evaluated query count is the direct answer to “rearrange the mean reciprocal rank relationship and solve for evaluated query count.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
sum of first-relevant reciprocal ranks=64 and evaluated query count=100 produce mean reciprocal rank=0.64.
Where this model stops being reliable
It ignores relevant results appearing after the first.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Mean Reciprocal Rank: solve evaluated query count works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Mean Reciprocal Rank: solve evaluated query count uses b=a/c. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Averages and representative values
Representative values help you judge what the Mean Reciprocal Rank: solve evaluated query count inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Mean Reciprocal Rank: solve evaluated query count formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read mean reciprocal rank, sum of first-relevant reciprocal ranks.
- Evaluate the principal relationship: b=a/c.
- Return evaluated query count and check the domain conditions described above.
Python
from math import *
def mean_reciprocal_rank_solve_b(c, a) -> float:
return (a / c)
assert abs(mean_reciprocal_rank_solve_b(0.64, 64) - 100) < 1e-6 * max(1.0, abs(100))
C
#include <assert.h>
#include <math.h>
double mean_reciprocal_rank_solve_b(double c, double a) {
return (a / c);
}
int main(void) {
const double expected = 100;
const double actual = mean_reciprocal_rank_solve_b(0.64, 64);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double mean_reciprocal_rank_solve_b(double c, double a) {
return (a / c);
}
int main() {
constexpr double expected = 100;
const double actual = mean_reciprocal_rank_solve_b(0.64, 64);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double mean_reciprocal_rank_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global mean_reciprocal_rank_solve_b
section .text
mean_reciprocal_rank_solve_b:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
divsd xmm0, [rbp-8]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = mean_reciprocal_rank_solve_b(c, a)
result = (a / c);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, a_] := (a / c);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Mean Reciprocal Rank evaluated query count Solver. MW SysArc Tools. https://math.mwsysarc.com/statistics/mean-reciprocal-rank-evaluated-query-count-solver
MLA 9
MW SysArc. “Mean Reciprocal Rank evaluated query count Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/mean-reciprocal-rank-evaluated-query-count-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Mean Reciprocal Rank evaluated query count Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/mean-reciprocal-rank-evaluated-query-count-solver.
Harvard
MW SysArc (2026) ‘Mean Reciprocal Rank evaluated query count Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/mean-reciprocal-rank-evaluated-query-count-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_mean_reciprocal_rank_solve_b_2026,
author = {{MW SysArc}},
title = {Mean Reciprocal Rank evaluated query count Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/mean-reciprocal-rank-evaluated-query-count-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Mean Reciprocal Rank evaluated query count Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/mean-reciprocal-rank-evaluated-query-count-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Mean Reciprocal Rank: solve evaluated query count do?
Rearrange the mean reciprocal rank relationship and solve for evaluated query count.
How does the Mean Reciprocal Rank: solve evaluated query count work?
The calculator applies b=a/c. Mean reciprocal rank averages one divided by the rank of each query's first relevant result. This page isolates evaluated query count and verifies it in the original relationship.
What can I learn from the Mean Reciprocal Rank: solve evaluated query count?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .