Mode (statistics)
The mode is the value that appears most frequently in a dataset, making it the only measure of central tendency applicable to nominal (categorical) data. A dataset can be unimodal (one mode), bimodal (two modes), multimodal (many modes), or have no mode if all values are equally frequent. The mode is particularly useful in market research, fashion, and any context where the most common category or value is of interest.
Worked Example
Problem
A shoe shop recorded the following shoe sizes sold in one day: 7, 8, 9, 8, 10, 8, 7, 9, 8, 11, 6, 8. Find the mode.
Solution
Step 1: List values and count frequency: Size 6: 1 time Size 7: 2 times Size 8: 5 times Size 9: 2 times Size 10: 1 time Size 11: 1 time Step 2: The value with highest frequency is Size 8 (5 times).
Answer
Mode = Size 8
Types of Modal Distribution
| Type | Description | Number of Modes | Example |
|---|---|---|---|
| Unimodal | One clear peak | 1 | Normal distribution |
| Bimodal | Two peaks | 2 | Heights of adults (men + women combined) |
| Multimodal | More than two peaks | > 2 | Multi-shift factory output |
| No mode | All values equally frequent | 0 | Uniform distribution {1,2,3,4,5,6} |
| Amodal | No repeated values | None | Unique ID numbers |
Interactive Tools
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Related Terms
Mean (statistics)
The mean (arithmetic mean) is the sum of all values in a dataset divided by the number of values, and represents the central or typical value. It is the most commonly used measure of central tendency and is sensitive to extreme values (outliers). The mean is used extensively in data analysis, quality control, and as the foundation for more advanced statistical measures such as variance and standard deviation.
Median
The median is the middle value of a dataset when values are arranged in ascending or descending order; it divides the distribution into two equal halves. For an even number of values, it is the average of the two central values. The median is a robust measure of central tendency, unaffected by extreme outliers, making it preferable to the mean for skewed distributions such as income or house prices.
Probability Distribution
A probability distribution is a mathematical function that describes the likelihood of each possible outcome of a random variable. It assigns a probability to every possible value or range of values that the variable can take, with all probabilities summing to 1. Probability distributions are foundational in statistics and are used in fields ranging from insurance and finance to physics and machine learning.
From French mode and Latin modus (measure, manner, way). In statistics, it refers to the most fashionable or frequent value. The statistical use was established in the 19th century alongside other measures of central tendency.