# Central Tendency, Citation Distributions, and Springer Nature (Part 2) | Ross Mounce

#### flavoursofopenscience's bookmarks 2021-11-19

### Summary:

“In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution. Colloquially, measures of central tendency are often called averages. The most common measures of central tendency are the arithmetic mean, the median, and the mode.” — Wikipedia.

In the UK, we teach school kids how to calculate the mean, median, and mode in Year 6 (kids aged 10-11), it’s simple stuff.

If your data is normally distributed then the mean is an appropriate measure of central tendency to describe your data. However, if your data has significant skew and/or big outliers then it is not considered appropriate to report the mean, and instead one should use the median or mode.

You’ll see this advice in countless stats textbooks and websites e.g.

“

In a strongly skewed distribution, what is the best indicator of central tendency?It is usually inappropriate to use the mean in such situations where your data is skewed. You would normally choose the median or mode, with the median usually preferred.” — from Laerd Statistics.In the Penn State “Elementary Statistics” course they teach that: “For distributions that have outliers or are skewed, the median is often the preferred measure of central tendency because the median is more resistant to outliers than the mean.”

In the SpringerNature “white paper” titled “Going for gold: exploring the reach and impact of Gold open access articles in hybrid journals” by Christina Emery, Mithu Lucraft, Jessica Monaghan, David Stuart, and Susie Winter, the authors examine the distribution of citations to 60,567 individual articles within 1,262 of Springer Nature’s ‘hybrid’ journals. To help understand the central tendency or ‘average’ of citations accrued to articles, the authors of this report frequently chose to refer-to and display means. The main figures of the paper (figures 1, 2, and 3) are particularly peculiar as they are bar chart style comparisons of means and model predictions.

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