Data
A set of facts that includes numbers, words, measurements, observations, and even simple descriptions of things is called data.
What is the Mode in Statistics?
The mode is the most frequently observed value in a set of data in statistics. The mode, like the mean and median, is the same value for a normal distribution. In many cases, the modal value will be different from the average value of a dataset.
Steps to Find the Mode
The steps to find the modes are as follows:
Step 1: Write the data set in ascending order.
Step 2: Find the frequency of the data that occurs most frequently in the given data set.
Types of Modes
There are three types of modes:
- Bimodal
When a data set contains two modes, it is referred to as bimodal.
For example, The mode of Set S = {4, 4, 4, 6, 9, 9, 21, 21, 21} is 4 and 21, because both 4 and 21 are repeated three times in the given set.
- Trimodal
When a data set contains three modes, it is referred to as trimodal.
For example, the mode of set S = {12, 12, 12, 31, 42, 42, 54, 54, 54, 78, 81, 81, 81} is 12, 54 and 81.
- Multimodal
When a data set contains four or more modes, it is referred to as multimodal.
Solved Examples
Example 1: Determine the data set’s mode: 1, 2, 3, 3, 6, 15, 15, 15, 27, 27, 37, 83.
Solution: Following is a list of numbers:
1, 2, 3, 3, 6, 15, 15, 15, 27, 27, 37, 83.
The number 15 is the mode because it appears more frequently in the set than the other numbers.
Example 2: Find the mode of the given data set 4, 4, 4, 8, 15, 15, 15, 27, 32, 48.
Solution: The data set is 4, 4, 4, 8, 15, 15, 15, 27, 32, 48.
A data set or set of values can have more than one mode, as we know. This happens when more than one value occurs with equal frequency and the number of times as a few other values in a set. As a result, the numbers 4 and 15 are both modes of the set in this case.
Example 3: Find the mode in 1, 4, 6, 7, 8, 34, and 64.
Solution: A data set is said to have no mode if no value or number appears more than once. As a result, there is no mode for sets 1, 4, 6, 7, 8, 34, and 64.
Example 4: The list depicts the types of sports that students in a class enjoy playing. Make a table with the information. Then look for the mode.
Solution: We have to create a table using the given data that depicts the number of students playing their favorite games:
So, soccer is played by the majority of students. Hence, the mode in this example is Soccer.
Example 5: The table shows the prices of six art portraits from an online store. When shipping is factored in, the price of each portrait rises by $5. What effect does this increase in price have on the mode of the data?
Solution: The mode of the given data for the initial prices is $120 because it occurs two times in the given data sets.
Add $5 to each price to make a new table. Then, for both data sets, determine their mode.
Now, we can find the measure of the center of both data sets.
Mode: 125 – 120 = $5
Hence, the mode will increase by $5 dollars if the shipping charges are included.
In statistics, a mode is defined as the value with the highest frequency among a set of values. It’s the value that shows up most frequently in some data.
It is said to be a no mode condition when a given set of observations has no value that is repeated more than once in the set.
If we have 21, 41, 55, 55, 62 as a set of numbers. The most frequently occurring value in the given set is 55. As a result, the given set’s mode is 55