Learn

In this lesson, you learned how to calculate the average of a dataset using the formula:

$\bar{x} = \frac{x_1 + x_2 … + x_{n}}{n}$

and the R function:

mean(my_data)

Circling back to the original question, do you feel like the average of our dataset, 42.12, provides us enough information to claim when someone is their most creative and productive?

Take a look at the histogram and mean (in red) to the right as you consider this question.

We would say, No. Though we could argue against its use for a few reasons, below, we’ve highlighted two:

• The date of publication is not necessarily an author’s most creative year. When did they start authoring the book? What factors impacted their writing during those years?
• The average age of the publishing dates for 100 authors may not accurately measure peak creativity in other professions. The average age of painters or sculptors may be very different.

So, what kind of information does the average provide us, and why would we use the average to describe something when we could display a histogram?

The most important outcome is that we’re able to use a single number as a measure of centrality. Although histograms provide more information, they are not a concise or precise measure of centrality — the reader must interpret it for themselves.

### Instructions

Take a look at the histogram to the right. Are you older or younger than the average age at publication?

This doesn’t tell you much about when someone will have their most creative year. However, this type of data could be used as an example in a broader study on aging.