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Related Concept Videos

Arithmetic Mean01:08

Arithmetic Mean

The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the data set, divided by the total number of elements. It is sometimes loosely referred to as the “average.”
When all the values in a data set are not unique, the sum in the numerator can be calculated by multiplying each distinct value by its frequency.
Sometimes, the arithmetic mean of a sample can be affected by a few data points that are...
Weighted Mean00:57

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
Trimmed Mean01:10

Trimmed Mean

While measuring the mean of a data set, care needs to be taken when associating the mean to its central tendency. The same goes for the arithmetic mean, the geometric mean, or the harmonic mean. This is because the presence of a single outlier data value can significantly affect the mean. That is, the mean is sensitive to fluctuations in the data set.
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the...
Geometric Mean01:15

Geometric Mean

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...
Mean From a Frequency Distribution01:11

Mean From a Frequency Distribution

Sometimes, data gathered from an experiment on a large sample or population are organized into concise tables. In such cases, the frequency of the quantitative data set is plotted in the form of a table. Or else, the data values are grouped into the quantity’s intervals, which form classes, and their respective frequencies are known. That is, the data values are distributed over different categories or classes. This is known as frequency distribution.
When such a data set is encountered, the...
Mean Absolute Deviation01:13

Mean Absolute Deviation

The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to...

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How Mean is the Mean?

Craig P Speelman1, Marek McGann

  • 1School of Psychology and Social Science, Edith Cowan University, Joondalup WA, Australia.

Frontiers in Psychology
|July 27, 2013
PubMed
Summary
This summary is machine-generated.

Psychological research should critically assess the use of the mean as a summary statistic. Over-reliance on the mean can lead to errors due to unmet assumptions, necessitating alternative research methods.

Keywords:
averagecognitiondistributional analysesmeannoisevariability

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Area of Science:

  • Psychology
  • Statistics

Background:

  • The mean is frequently used as a summary statistic in psychological research.
  • Its uncritical application overlooks underlying assumptions and potential violations.

Purpose of the Study:

  • To highlight concerns regarding the pervasive and uncritical use of the mean in psychological research.
  • To examine the implicit assumptions tied to the mean and their fragility.
  • To explore alternative, less mean-dependent research methodologies.

Main Methods:

  • Critical analysis of the assumptions inherent in using the mean.
  • Examination of theoretical and methodological errors arising from violated assumptions.
  • Illustration of alternative research models within psychology.

Main Results:

  • The uncritical use of the mean can lead to significant theoretical and methodological errors.
  • Fragile assumptions underlying the mean require more careful consideration.
  • Alternative research approaches can mitigate reliance on the mean.

Conclusions:

  • Psychological research should adopt a more critical stance towards the use of the mean.
  • Study design and review processes should explicitly assess assumptions related to the mean.
  • Exploring less mean-dependent methods is crucial for robust psychological research.