Mean Log Deviation¶
In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality.
Core Idea¶
Mean Log Deviation is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality. In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality. The MLD is zero when everyone has the same income, and takes larger positive values as incomes become more unequal, especially at the high end. where N is the number of households, xi is the income of household i, and \overline{x} is the mean of.
Scope of Application¶
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The MLD of household income has been defined as. Naturally the same formula can be used for positive variables other than income and for units of observation other than households.
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The MLD of household income has been defined as. \mathrm{MLD}=\frac{1}{N}\sum{i=1}^N \ln \frac{\overline{x}}{xi}.
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The MLD of household income has been defined as. where N is the number of households, xi is the income of household i, and \overline{x} is the mean of xi .
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Equivalent definitions are. \mathrm{MLD}=\frac{1}{N}\sum{i=1}^N (\ln \overline{x} - \ln xi).
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Equivalent definitions are. The last definition shows that MLD is nonnegative, since \ln{\overline{x}} \geq \overline{\ln x} by Jensen's inequality.
Clarity¶
A clear use of Mean Log Deviation names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality. The strongest recognition evidence in the frozen account is: Naturally the same formula can be used for positive variables other than income and for units of.
Manages Complexity¶
Mean Log Deviation compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—\mathrm{MLD}=\frac{1}{N}\sum{i=1}^N \ln \frac{\overline{x}}{xi}.—and the practical consequence—mLD has been called "the standard deviation of ln(x)", (SDL) but this is not correct. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit.
Abstract Reasoning¶
- Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
- State the relation. Use the source-grounded identity: In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality.
- Check operation and conditions. where N is the number of households, xi is the income of household i, and \overline{x} is the mean of xi .
- Demand recognition evidence.
Knowledge Transfer¶
Within the home domain. Knowledge about Mean Log Deviation transfers literally when a new case preserves the same carrier type, relation, and recognition test. Naturally the same formula can be used for positive variables other than income and for units of observation other than households. \mathrm{MLD}=\frac{1}{N}\sum{i=1}^N \ln \frac{\overline{x}}{xi}. Beyond the home domain. No canonical parent is asserted for Mean Log Deviation.
Neighborhood in Abstraction Space¶
Mean Log Deviation sits in a moderately populated region (43rd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Service-Quality Rates & Queueing Metrics (13 abstractions)
Nearest neighbors
- S-procedure — 0.89
- Big O in probability notation — 0.87
- Scale parameter — 0.86
- Binade — 0.86
- Filling radius — 0.86
Computed from structural-signature embeddings · 2026-10-08