Learn how to calculate measures of central tendency for different types of data.
Example 1: Mean for Ungrouped Data
Find the mean of the following data: 10, 20, 30, 40, 50
Concept: The Mean (or average) of ungrouped data is the sum of all observations divided by the number of observations.
Mean = (Sum of observations) / (Number of observations)
Step 1: Sum the given observations.
Sum = 10 + 20 + 30 + 40 + 50 = 150
Step 2: Count the number of observations.
Number of observations = 5
Step 3: Calculate the Mean.
Mean = 150 / 5 = 30
Example 2: Median for Ungrouped Data (Odd Number of Observations)
Find the median of the following data: 15, 12, 18, 13, 17
Concept: The Median is the middle value of a data set when it is arranged in ascending or descending order. For an odd number of observations, the median is the single middle value.
Step 1: Arrange the data in ascending order.
Ordered Data: 12, 13, 15, 17, 18
Step 2: Identify the middle value. There are 5 observations, so the middle value is the 3rd term.
Middle value = 15
Result: The Median is 15.
Example 3: Median for Ungrouped Data (Even Number of Observations)
Find the median of the following data: 10, 20, 30, 40, 50, 60
Concept: For an even number of observations, the median is the average of the two middle values after the data is arranged in order.
Step 1: Arrange the data in ascending order.
Ordered Data: 10, 20, 30, 40, 50, 60
Step 2: Identify the two middle values. There are 6 observations, so the middle values are the 3rd and 4th terms.
Middle values are 30 and 40.
Step 3: Calculate the average of the two middle values.
Median = (30 + 40) / 2 = 70 / 2 = 35
Result: The Median is 35.
Example 4: Mode for Ungrouped Data
Find the mode of the following data: 5, 7, 8, 7, 5, 6, 7, 9
Concept: The Mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), more than one mode (multimodal), or no mode.
Step 1: Count the frequency of each observation.
5 appears 2 times.
6 appears 1 time.
7 appears 3 times.
8 appears 1 time.
9 appears 1 time.
Step 2: Identify the observation with the highest frequency.
The highest frequency is 3, which corresponds to the value 7.
Result: The Mode is 7.
Practice Mode
Enter a list of numbers separated by commas to calculate the Mean, Median, and Mode.
Note: This basic solver works for ungrouped data only.
Related Concepts
Explore these related mathematical concepts to deepen your understanding of Statistics.
Data
A collection of facts or information, such as numbers, words, measurements, observations, or just descriptions of things.
Observation
A single data point or value in a data set.
Frequency
The number of times a particular observation occurs in a data set.
Ungrouped Data
Raw data that has not been organized into categories or classes.
Grouped Data
Data that has been organized into groups or classes with corresponding frequencies.
Measures of Central Tendency
Single values that attempt to describe a set of data by identifying the central position within that set (Mean, Median, Mode).
Mean
The average of a data set (sum of values divided by the number of values).
Median
The middle value in a data set when arranged in order.
Mode
The value that appears most frequently in a data set.
Range
The difference between the highest and lowest values in a data set.