In this lesson, you will learn how to find the mode of a dataset manually, and using base R.


Mode in R

Finding the mode of a dataset becomes increasingly time-consuming as the size of your dataset increases &mdash; imagine finding the mode of a dataset with 10,000 observations.

The R package `DescTools` includes a handy `Mode()` function which can do the work of finding the mode for us. In the example below, we use `Mode()` to calculate the mode of a dataset with ten values:


#### Example: One Mode

```R
library(DescTools)

example_data <- c(24, 16, 12, 10, 12, 28, 38, 12, 28, 24)

example_mode <- Mode(example_data)
```

The code above calculates the mode of the values in `example_data` and saves it to `example_mode`. 

The result of `Mode()` is a vector with the mode value:
```
>>> example_mode
[1] 12
```


#### Example: Two Modes

If there are multiple modes, the `Mode()` function will return them as a vector.

Let's look at a vector with two modes, `12` and `24`:

```R
example_data = c(24, 16, 12, 10, 12, 24, 38, 12, 28, 24)

example_mode = Mode(example_data)
```

The result is:
```R
>>> example_mode
[1] 12 24
```

Mode with DescTools

In this lesson, you will learn how to find the *mode* of a dataset. Each of the next three exercises will cover the following:
- Manually finding the mode of a dataset
- Using R's functions to find the mode
- Comparing mode to mean and median values

In the lesson, we will use a dataset of the 100 greatest novels, determined by a French literary magazine, Le Monde. From the dataset, you will use the mode to answer the question: 

*What is the most common age for a great author to publish their best work?*

If you are not familiar with mean, also known as average, or median, we recommend that you learn about it in our lessons on <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/average/exercises/introduction" target="_blank">average</a> and <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/median/exercises/introduction" target="_blank">median</a>.




Introduction

The formal definition for the mode of a dataset is:

*The most frequently occurring observation in the dataset. A dataset can have multiple modes if there is more than one value with the same maximum frequency.*

While you may be able to find the mode of a small dataset by simply looking through it, if you have trouble, we recommend you follow these two steps:
1. Find the frequency of every unique number in the dataset
2. Determine which number has the highest frequency

#### Example

Say we have a dataset with the following ten numbers: 
```tex
24,\ 16,\ 12,\ 10,\ 12,\ 28,\ 38,\ 12,\ 28,\ 24
```

Let's find the frequency of each number: 

<div class="narrative-table-container">

|*24*|*16*|*12*|*10*|*28*|*38*|
|-|-|-|-|-|-|
|2|1|3|1|2|1|

</div>
    

From the table, we can see that our mode is `12`, the most frequent number in our dataset. 


Mode

In this lesson, you learned how to find the mode of a dataset in two steps:
1. Find the frequency of every unique number in the dataset
2. Determine which number has the highest frequency

You also learned how to calculate the mode using DescTools:
```R
Mode(my_array)
```

#### Discussion

In this lesson, you found that 38 was the most common age, at publication, for an author from the Le Monde survey. How does this number compare to your guess from the beginning of the lesson?

The mode is close to the median and mean of the dataset, but it is not in the tallest bucket. This should not be surprising, as the histogram indicates the data is centered between the ages of 30 and 50 &mdash; there is a higher chance of a mode in that range than outside of it.

The mode is not always this close to the median and mean, and often will not be in the tallest bucket.

Look at the 25-30 year-old bin. There are nine observations in it. If all the values in that bin happened to be 27, then the dataset's mode would be 27. Although unlikely, it is possible. Below, we show what this would look like:

![Mode set to 27](https://content.codecademy.com/courses/statistics/mode/mode-at-27.png)

Based on this graph, it is fair to say the mode may not always be a great measure of where the data is centered. Simply put, mode is a measure of the most frequent observation in the dataset, and is not an indication of the tallest bin in a histogram.

In the instructions below, we've written a brief explanation that puts mode in the context of our problem.

