**Mode Formula and Mean**

Nowadays it is a challenging task for many of us to find a current tendency in many fields such as the medical field, marketing, etc. To find this we need to collect the information from the customer and analyse the data collected in a particular field and interpret which would be more frequently used by more customers this is a mathematical representation called statistics. In statistics we will gather the information, analyse, interpret and present the current tendency of customers in a particular field. We often use the mode formula for that.

It is a tedious job to gather the information of particular data and find the current tendency in a particular field. STATISTICS is a branch of mathematics that deals with current trends in particular fields. To know the current tendency we find the mode, mean, median, and also range.

**Definition of Mode**

Mode refers to the score with the highest frequency, taking place many times. Mode can be found for grouped and ungrouped data. Mode is a collection of scores or classes that occur frequently or more than a number of times. Suppose for example we visit the hospital to collect the data related to checking the frequency of patients admitted with a particular disorder. Initially, we visit the different departments such as general medicine, orthopedic, pediatrics, cardiology, neurology, etc present in hospital collect the data of patients consulted particular department, analyse or understand the data to which department the patients visited most, interpret the data and represent the data set of a particular department. The table below shows the data set of hospitals of particular departments:

Department | General medicine | Cardiology | Orthopedic | Pediatrics | Neurology |

No. of patients | 40 | 23 | 15 | 30 | 10 |

In the above data set given, more patients consult general medicine so the mode of the class is considered to be 40, which means most patients visit. Mode could be grouped with a fixed interval or range and ungrouped.

**Mode For Ungrouped Data**

The following steps are involved in finding the mode for ungrouped data

- Observe the data set that occurs more frequently.
- Order the data from small to large.
- If the data occurs more frequently then it is considered to be in ungrouped data.

For eg: Find the mode for ungrouped data of a given data set 3,6,4,3,2,4,7,8,6,3,9.

Order of the given data set : 2,3,3,3,4,4,6,6,7,8,9.

Observe the data that occurs most frequently. Here, in the above data set 3 occurs more frequently than other data so 3 is considered to be the mode of the given ungrouped data set. Mode = 3

**Mode For Grouped Data**

Grouped data is defined as the data with fixed intervals. Mode can be calculated for grouped data using the below formula.

#### FORMULA TO FIND MODE FOR GROUPED DATA

#### Mode = +

#### Where l = lower limit of class

h = size of class interval

f = frequency of class

f1 = previous frequency of class

f2 = next frequency of class

##### EXAMPLE FOR MODE CALCULATION OF GROUPED DATA

Calculate the mode for given grouped data of a class:

marks | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |

No. of students | 7 | 10 | 12 | 6 | 4 |

FORMULA: Mode =

Here, in the above example l = 40, h = 20, f = 12, f1 = 10 and f2 = 6

So, Mode = = 40+20/8 = 40 + 2.5

MODE = 42.5

For more such interesting mathematical concepts, let’s visit the Cuemath website.

**MEAN**

Mean is defined as the average of data. It is found by dividing the sum of data values by the total no. of observations. Generally in our daily life, we use this while finding the average height of people, average of marks, etc.

### Mean=

EXAMPLE: To calculate the mean for a given data set consisting of the data value in chemistry or physics lab in an experiment.

Values found in lab = 10, 20, 30, 40, 50

Mean = = = 20