Mode

Child: Let’s say you and your friends are talking about your favorite colors. The mode is simply the color that is said the most. So, if most of your friends say their favorite color is blue, then the mode is blue!
Teenager: Imagine you’re in a class and the teacher asks everyone what their favorite book is. Some people might say the same book, and some might have different favorites. The mode is the book that gets mentioned the most times. It’s the most popular or common answer in the group.
Undergrad majoring in the same subject: The mode is a statistical term that refers to the most frequently occurring number in a data set. A data set may have one mode, more than one mode, or no mode at all. It’s one of the measures of central tendency, along with mean and median. It is particularly useful for categorical data.
Grad student: In statistics, the mode is a type of average, used alongside the mean and median. It’s the value that appears most frequently in a data set. Unlike the mean and median, the mode can be used for both numerical and categorical data. For numerical data, it can help identify peaks in data distribution, and for categorical data, it can reveal the most common category.
Colleague (Fellow Researcher/Engineer): As you know, the mode is a valuable measure of central tendency, especially when dealing with non-numerical or nominal data. It identifies the most frequently occurring value in a dataset, providing crucial insights into the data’s distribution. Furthermore, in multimodal distributions, identifying multiple modes can shed light on the presence of distinct groups within our data. However, it’s worth noting that the mode can sometimes be misleading in the presence of outliers or when the dataset is sparse.

The mode refers to the value that appears most frequently in a dataset. A set may have one mode, multiple modes, or no mode.

To find the mode:

Count frequency of each unique value
The value(s) with the highest frequency are the mode(s)

Java example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
int mode(int[] nums) {
  Map<Integer, Integer> freq = new HashMap<>();

  for (int n : nums) {
    freq.put(n, freq.getOrDefault(n, 0) + 1); 
  }

  int maxFreq = 0;
  int mode = 0;
  for (Map.Entry<Integer,Integer> entry : freq.entrySet()) {
    if (entry.getValue() > maxFreq) {
      mode = entry.getKey();
      maxFreq = entry.getValue();
    }
  }

  return mode;
}

C++ example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
int mode(vector<int> nums) {
  unordered_map<int, int> freq;

  for (int n : nums) {
    freq[n]++;
  }

  int maxFreq = 0;
  int mode = 0;

  for (auto entry : freq) {
    if (entry.second > maxFreq) {
      mode = entry.first;
      maxFreq = entry.second;
    }
  }

  return mode;
}

Python example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
from statistics import mode

def data_mode(nums):
  return mode(nums)

# Or manually:

def manual_mode(nums):
  freq = {}
  for n in nums:
    freq[n] = freq.get(n, 0) + 1
  
  max_freq = max(freq.values())

  for n, f in freq.items():
    if f == max_freq:
      return n 

The mode shows the most common or frequent value(s) in a dataset. Useful for probability distributions.

Mode

Concept

The Mode is a statistical measure that identifies the most frequently occurring value in a data set. In a list of numbers, the mode is the number that appears most often. A data set can have zero or more modes. If all numbers appear equally frequently, the set has no mode.

Key Takeaways

Mode identifies the most frequent value.
A data set can have multiple modes or none.
Used in statistical analysis.

Example Code

Here’s how you can find the mode of an array of integers in different programming languages.

Java

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
import java.util.HashMap;

public class ModeFinder {
    public static int findMode(int[] arr) {
        HashMap<Integer, Integer> countMap = new HashMap<>();
        for (int num : arr) {
            countMap.put(num, countMap.getOrDefault(num, 0) + 1);
        }

        int mode = arr[0];
        int maxCount = 1;
        for (int key : countMap.keySet()) {
            if (countMap.get(key) > maxCount) {
                maxCount = countMap.get(key);
                mode = key;
            }
        }
        return mode;
    }

    public static void main(String[] args) {
        int[] arr = {1, 2, 2, 3};
        System.out.println(findMode(arr));
    }
}

C++

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
#include <iostream>
#include <unordered_map>

int findMode(int arr[], int n) {
    std::unordered_map<int, int> countMap;
    for (int i = 0; i < n; ++i) {
        ++countMap[arr[i]];
    }

    int mode = arr[0];
    int maxCount = 1;
    for (auto& pair : countMap) {
        if (pair.second > maxCount) {
            maxCount = pair.second;
            mode = pair.first;
        }
    }
    return mode;
}

int main() {
    int arr[] = {1, 2, 2, 3};
    std::cout << findMode(arr, 4);
    return 0;
}

Python

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
from collections import Counter

def find_mode(arr):
    count_map = Counter(arr)
    mode = arr[0]
    max_count = 1

    for key, value in count_map.items():
        if value > max_count:
            max_count = value
            mode = key

    return mode

arr = [1, 2, 2, 3]
print(find_mode(arr))

In each example, we use a hash map to count the occurrences of each integer. We then find the key with the highest value to identify the mode.