**Mode Formula**: Mode is one of the values that indicate a central tendency of a set of data. Mode or modal value gives us an idea about which of the items in a data set tend to occur most frequently. We can find Mode of a data with normal data set, group data set and non-grouped or ungrouped data set. Depending on the type of the dataset given, you can find one, two three or even multiple modal values. Some data sets may have no mode value at all. Before going into the mathematical formula for finding mode, let us take a look at an example to understand what mode is a bit more clearly:

The runs scored by a batsman in 10 cricket matches are as follows:

2 | 10 | 25 | 10 | 44 | 55 | 10 | 1 | 0 | 50 |

Mode is given as the value among the observation that occurs most often. So, the mode of this data is 10.

In this article, we will provide you with all the details regarding Mode Formula, mode calculation, solved example and other relevant details.

## What Is Mode Formula?

The formula used to find the mode of a grouped or non-grouped data is called mode formula and the value of the observation having the maximum frequency is called mode.

Mode = l +\(\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)

Where,

l = lower limit of the modal class

h = size of the class interval

f_{1} = frequency of the modal class

f_{0} = frequency of the class preceding the modal class

f_{2} = frequency of the class succeeding the modal class

Let us help you understand and use the above formula effectively through an example.

## Mode Formula With Examples

If the data is ungrouped finding mode is very easy as it is the value that appears the most often. An example of such type is:

**Mode Of Ungrouped Data**

**Sample Problem 1: Find the mode of the given data set: 4, 4, 6, 10, 18, 18, 18, 30, 30, 40, 51.**

**Solution:** In the following list of numbers 4, 4, 6, 10, 18, 18, 18, 30, 30, 40, 51. 18 appears the maximum number of time and therefore is the mode.

**Sample Problem 2: Find the mode of 5, 5, 5, 10, 16, 16, 16, 28, 38, 49 data set**.

**Solution:** In the given data set both 5 and 16 appear the max number of time i.e. 3 therefore, the mode is both 5 and 15.

**Fact Update:** a given data set or values can have more than one mode if more than one value occurs with equal frequency and number of time compared to the other values in the set.

**Sample Problem 3: Find the mode of 2, 5, 8, 15, 26, 36, 47.**

**Solution:** There can be data set that do not have a mode and one such example is the above question

So, for data set 2, 5, 8, 15, 26, 36, 47 there is no mode available.

**Mode Of Grouped Data**

Now we will take the example of grouped data and how to use the above explained formula to calculate mode.

**Example 1:** **A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household: **

Family Size | 1 – 3 | 3 – 5 | 5 – 7 | 7 – 9 | 9 – 11 |

Number of Families | 7 | 8 | 2 | 2 | 1 |

**Find the mode for the above data.**

**Solution 1:** Here the maximum class frequency is 8, and the class corresponding to this frequency is 3 – 5. So, the modal class is 3 – 5.

Now

– Modal class = 3 – 5, lower limit (l) of modal class = 3, class size (h) = 2

– Frequency (f_{1}) of the modal class = 8, frequency

– (f_{0}) of class preceding the modal class = 7,

– Frequency (f_{2}) of class succeeding the modal class = 2.

Putting the values in the formula:

Mode = l +\(\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)

Mode = 3 +\(\frac{8-7}{2×8-7-2}\times 2\) = 3.286.

## Mean Median Mode Formula

In your home exams, you will be asked to calculate all 3 i.e mean, median, and mode for a given data set:

Mean | Median | Mode |

Mean for observations id given as: \(\frac{Sum of observations}{Number of observations}\). | Median is calculated for a given range or data set by arranging the values in ascending or descending order and then taking the middle value. | Mode is the value that is repeated the maximum number of times. |

Let us consider the following data set 3, 3, 5, 6, 8.

Mean = (3+4+5+6+8)/5 = 5.2 | Median = 5 | Mode = 3 |

Now you know the basic formula to calculate the mode of a dataset. However, it is important to understand the concepts behind mode thoroughly and do more practice to master this important topic. Embibe offers interactive and fun videos that will help students to learn difficult concepts easily. Watch these videos to understand mode and several other mathematics topics in depth.

## FAQs On Mode Formulas

Here are some relevant questions on the topic:

Q1. What is the formula for mode and median?Ans. The formula for median and mode is:Median: [(n/2) (when n is even) ^{th} term + {(n/2)+1}^{th} term]/2{(n+1)/2} (when n is odd)^{th} termMode = l +\(\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\) |

Q2. How do you use the Mode formula? Ans. How to effectively use the formula has been explained with an example on this page. The formula is only valid for grouped data as for ungrouped data you can find the mode by directly looking at the data set. |

Q3. How do you find the mode in a frequency table? In a frequency table, you must find the values of the various elements of the mode formula and then put the values in the formula to calculate the mode.Ans. |

* Want help with more formulas? Check out some more formulas given below*.

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*Hope you enjoyed learning about Mode Formulas, and the information provided here answered all your questions. However, if you have further doubts feel free to use the comments section and we will provide you with an update. *

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