18. Lexical Diversity

Continuity

The richness and variety of vocabulary in Kifuliiru communications.

L D S = \frac{V _{u ni q u e}}{N _{t o t a l}}

Data & measurement

Continuity metrics emphasize intergenerational transmission, corpus completeness, and structural stability. Keep cohort definitions fixed across measurement waves. Symbols: LDS (Lexical Diversity Score (0 to 1)); V_unique (Count of unique/distinct words used); N_total (Total number of words in the sample). Log instrument versions, sample frames, and cleaning rules whenever estimates are refreshed so longitudinal comparisons stay valid.

Solution & proof

Conceptual summary: The richness and variety of vocabulary in Kifuliiru communications. Treat this as a measurement recipe: map each symbol to an empirical quantity, substitute estimates, and simplify with ordinary algebra (including logarithms, min/max caps, or piecewise branches where shown). Where limits or integrals appear, approximate with discrete sums on cohorts or time steps when closed forms are impractical. Interpret the result against thresholds in the cited source and report uncertainty on inputs.

Examples

1. Word problem — field log
Word problem
A measurement round produced the table below. Each symbol matches the Variables section for “Lexical Diversity”. Find the computed value using the formula above.
Illustrative inputs—replace with your field numbers
Quantity Symbol Value
Lexical Diversity Score (0 to 1) LDS 0.52
Count of unique/distinct words used V_unique 0.63
Total number of words in the sample N_total 750
Solution
Step 1 — From the table, assign LDS = 0.52; V_unique = 0.63; N_total = 750.
Step 2 — Substitute into the definition of “Lexical Diversity” at the top of the page (same structure as the source formula).
Step 3 — Finish any remaining algebra (sums, caps, logs, or limits) by hand or in a CAS when the expression still contains Σ, integrals, or non-numeric parameters. Tie final numbers back to your corpus or community records.
$Given: L D S = 0.52, V_{u} ni q u e = 0.63, N_{t} o t a l = 750 L D S = \frac{V _{u ni q u e}}{N _{t o t a l}}$
2. Second scenario — adjusted inputs
Word problem
The same measure applies with corrected inputs for the next report (see table). Recompute using the same formula.
Revised values for the next report (illustrative)
Quantity Symbol Value
Lexical Diversity Score (0 to 1) LDS 0.47
Count of unique/distinct words used V_unique 0.63
Total number of words in the sample N_total 750
Solution
Step 1 — From the table, assign LDS = 0.47; V_unique = 0.63; N_total = 750.
Step 2 — Substitute into the definition of “Lexical Diversity” at the top of the page (same structure as the source formula).
Step 3 — Finish any remaining algebra (sums, caps, logs, or limits) by hand or in a CAS when the expression still contains Σ, integrals, or non-numeric parameters. Tie final numbers back to your corpus or community records.
$Given: L D S = 0.47, V_{u} ni q u e = 0.63, N_{t} o t a l = 750 L D S = \frac{V _{u ni q u e}}{N _{t o t a l}}$

Quantity	Symbol	Value
Lexical Diversity Score (0 to 1)	LDS	0.52
Count of unique/distinct words used	V_unique	0.63
Total number of words in the sample	N_total	750

Quantity	Symbol	Value
Lexical Diversity Score (0 to 1)	LDS	0.47
Count of unique/distinct words used	V_unique	0.63
Total number of words in the sample	N_total	750

Variables

Symbol	Description
`LDS`	Lexical Diversity Score (0 to 1)
`V_unique`	Count of unique/distinct words used
`N_total`	Total number of words in the sample

Source

ALL_FORMULAS.md — Continuity

Data & measurement

Solution & proof

Examples

1. Word problem — field log

2. Second scenario — adjusted inputs

Variables

Source

Tags