In this lesson, you will learn how to calculate the average of a dataset by hand, and use R  to calculate to calculate it for you. We will also discuss the strengths and limitations of using average as a summary statistic of a dataset.


Mean in R

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

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

and the R function:
```R
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 &mdash; the reader must interpret it for themselves.


Review and Discussion

While you've shown that you can calculate the average yourself, it becomes time-consuming as the size of your dataset increases &mdash; imagine adding all of the numbers in a dataset with 10,000 observations.

The R `mean()` function can do the work of adding and dividing for you. In the example below, we use `mean()` to calculate the average of a dataset with ten values:

```r
example_data <- c(24, 16, 30, 10, 12, 28, 38, 2, 4, 36)

example_average <- mean(example_data)

print(example_average)
```

The code above calculates the average of `example_data` and saves the value to `example_average`. The resulting average of this array is `20`.


The *mean*, often referred to as the *average*, is a way to measure the center of a dataset. 

The average of a set is calculated using a two-step process:
1. Add all of the observations in your dataset.
2. Divide the total sum from step one by the number of points in your dataset.

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

The equation above is used to calculate mean. `x1`, `x2`, ... `xn` are observations from a dataset of `n` observations. 


#### Example

Imagine that we wanted to calculate average of a dataset with the following four observations:
```R
data <- c(4, 6, 2, 8)
```
##### Step One: Calculate the total

```tex

4 + 6 + 2 + 8 = 20

```

##### Step Two: Divide by the number of observations

The total is equal to 20, and the number of observations is equal to 4.
```tex
\frac{20}{4} = 5
```

The average of this dataset is equal to 5.


Calculating Mean

Finding the center of a dataset is one of the most common ways to summarize statistical findings. Often, people communicate the center of data using words like, *on average*, *usually*, or *often*.

In this lesson, you will learn how to calculate the *mean* of a dataset, a common measure of a dataset's center. We will use the mean to help us answer the question, 

*When are adults their most creative and productive?*

You could define "creative" and "productive" in a lot of ways, making this question impossible to fully answer by the end of this lesson. However, you will form an informed opinion on the question using data of the one hundred greatest novels of all time. 

We collected the dataset from a survey administered by the French literary magazine, Le Monde. From the dataset, you will calculate the average age of the authors when their books were published.
