The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean (average) and the median (middle value).
Key Takeaways
- In statistics, the mode is the most commonly observed value in a dataset.
- For the normal distribution, the mode is also often the same value as the mean and median.
- In many cases, the modal value will differ from the average value in the data set.
Understanding the Mode
Data in statistics can be distributed in various ways. The most often cited distribution is the classic normal (bell-curve) distribution. In such a distribution, the mean (average) value falls at the midpoint, which is also the peak frequency of observed values. For such a distribution, the mean, median, and mode are all the same value. This means that this value is the average value, the middle value, and also the mode—the most frequently occurring value in the data.
The mode is particularly useful as a measure of central tendency when examining categorical data, such as models of cars or flavors of soda, where a mathematical average or median based on ordering cannot be calculated.
Examples of the Mode
For example, in the following list of numbers, 16 is the mode since it appears more times in the set than any other number:
- 3, 3, 6, 9, 16, 16, 16, 27, 27, 37, 48
A dataset can have more than one mode (this is known as bimodal if there are two modes) if there are multiple numbers that occur with equal frequency and more times than the others in the set. For instance:
- 3, 3, 3, 9, 16, 16, 16, 27, 37, 48
In this example, both the number 3 and the number 16 are modes as they each occur three times and no other number occurs more often.
If no number in a set of numbers occurs more than once, that set has no mode:
- 3, 6, 9, 16, 27, 37, 48
A set of numbers with two modes is bimodal, a set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal. When scientists or statisticians refer to the modal observation, they are referencing the most common observation.
Mode vs. Mean vs. Median
The mode, mean, and median are all different ways of noting the center of a data set.
- Mode: The most common value.
- Mean: The average of the values.
- Median: The middle value when the data set is ordered.
Mean
The mean is the average of a set of numbers. To calculate it, add up all the data points and divide by the total number of points. For example, for the series of numbers:
- 3, 3, 6, 9, 16, 16, 16, 27, 27, 37, 48
The sum is 208. Dividing 208 by 11 (the number of data points) gives a mean of 18.9.
Median
The median is the data point in the middle of an ordered set. Arrange the numbers from smallest to largest:
- 3, 3, 6, 9, 16, 16, 16, 27, 27, 37, 48
The median is 16, the data point in the exact middle. For an even number of data points, you take the mean of the two middle numbers to find the median.
Advantages and Disadvantages of the Mode
Advantages
- The mode is easy to understand and calculate.
- It is not affected by extreme values.
- Identifiable in both a dataset and a discrete frequency distribution.
- Useful for qualitative data.
- Can be computed in an open-ended frequency table.
- Locatable graphically.
Disadvantages
- Undefined in datasets with no repeats.
- Not based on all values.
- Unstable with small datasets.
- Sometimes, a dataset may have one mode, more than one mode, or no mode at all.
How Do I Calculate the Mode?
To calculate the mode, place all numbers in the data set in order (lowest to highest or highest to lowest), and then count how many times each number appears. The number that appears the most is the mode.
What Is Mode in Statistics With an Example?
In statistics, the mode refers to the number that appears most often in a set. For example, in the set 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode is 7, as it appears the most frequently.
What Is the Difference Between Mode and Mean?
The mode is the most frequently appearing number in a set of numbers. The mean is the sum of all numbers divided by the number of values, also known as the average.
The Bottom Line
In statistics, the mode identifies the number that occurs most often. A dataset can have one or more modes. The mode is different from the mean (the average) and the median (the midpoint). Determining the mode in a dataset reveals which data points occur most commonly, offering valuable insight when analyzing statistics.
Related Terms: mean, median, frequency distribution, central tendency, bimodal, trimodal, multimodal
