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Related Concept Videos

Measures of Central Tendency02:16

Measures of Central Tendency

18.8K
The "center" of a data set is also a way of describing location. The two most widely used measures of the "center" of the data are the mean (average) and the median. The words "mean" and "average" are often used interchangeably. The substitution of one word for the other is common practice. The technical term is "arithmetic mean" and "average" is technically a center location. However, in practice among non-statisticians,...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
8.5K
Geometric Mean01:15

Geometric Mean

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The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
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Regression Toward the Mean01:52

Regression Toward the Mean

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
6.6K
Testing a Claim about Mean: Known Population SD01:11

Testing a Claim about Mean: Known Population SD

3.0K
A complete procedure of testing the hypothesis about a population mean is explained here.
Estimating a population mean requires the samples to be distributed normally. The data should be collected from the randomly selected samples having no sampling bias. The sample size needed to be higher than 30, and most importantly, the population standard deviation should be already known.
In most realistic situations, the population standard deviation is often unknown, but in rare circumstances, when it...
3.0K
Skewness01:06

Skewness

15.7K
The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency...
15.7K

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Related Experiment Video

Updated: Nov 25, 2025

The Motivation for Alcohol Reward: Predictors of Progressive-Ratio Intravenous Alcohol Self-Administration in Humans
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Rising mean incomes for whom?

Liang Frank Shao1, Melanie Krause2

  • 1School of Economics, Henan University, Kaifeng, Henan, China.

Plos One
|December 16, 2020
PubMed
Summary

Rising incomes do not benefit everyone equally. The study introduces the mean-income population share (MPS) to assess if economic growth is inclusive, finding it often excludes middle-income households.

Area of Science:

  • Economics
  • Income Distribution Studies
  • Econometrics

Background:

  • Mean income growth does not always reflect equitable economic progress.
  • Assessing the inclusivity of economic growth requires examining its distribution across income levels.
  • Traditional metrics may not fully capture the representation of middle-income households during periods of rising average incomes.

Purpose of the Study:

  • To introduce and analyze the mean-income population share (MPS) as a metric for economic inclusivity.
  • To evaluate the extent to which rising mean incomes benefit middle and lower-income populations.
  • To compare analytical characterizations and parametric estimations of MPS and related metrics.

Main Methods:

  • Analytical characterization of MPS and mean income share (MIS) under various growth scenarios.

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  • Parametric estimation of MPS and MIS using both micro-level and grouped income data.
  • Empirical analysis using panel data from 16 high- and middle-income countries.
  • Main Results:

    • Rising mean incomes over recent decades have often not favored middle-income households in relative terms.
    • The evolution of MPS indicates varying degrees of inclusivity in economic growth across countries.
    • The relationship between MPS changes, income shares, and the Gini coefficient shows mixed welfare effects.

    Conclusions:

    • The mean-income population share (MPS) is a valuable indicator for assessing the distributional consequences of economic growth.
    • Economic growth's benefits are not uniformly distributed, with middle-income groups frequently not being primary beneficiaries.
    • Further research is needed to fully understand the complex interplay between income distribution metrics and overall welfare.