**Mean median mode formula**

**Small Description- **Mean is the arithmetic mean of the given data. Median is the middle value of the given data when it is assembled in ascending order. Mode is the value that gets repeated the most in data.

The mean is calculated as:

Sum of observations ÷ total number of observations

When ‘n’ is odd

The median is calculated as:

(n+1 ÷ 2)ᵀᴴ term

When ‘n’ is even

The median is calculated as:

(n÷2)ᵀᴴ term + (n÷2 +1)ᵀᴴ term ÷ 2

Mode is calculated as:

L + h × (fₘ-f₁) ÷ (fₘ-f₁) + (fₘ-f₂)

**Mean: **

The mean is calculated by dividing the sum of observations by the total number of observations. The mean is the average value of the given data.

**Median: **

The median is calculated by arranging the data in ascending or descending order.

The median for grouped data is calculated as:

Lₘ+ {(n ÷ 2 – f) / fₘ} × i

Lₘ is the lower boundary of the median class

n is the total frequency

f is the total frequency of the class before the median class

fₘ is the frequency of the median class

i is the width of the class

**Mode: **

A value that is repeated the most in data is called mode. In the data where there is no repeated value, there is no mode. The mode for data depends on the value of the dataset. The mode for the grouped data can be calculated as:

L + h × (fₘ-f₁) ÷ (fₘ-f₁) + (fₘ-f₂)

L = lower limit of the modal class

h= size of the class interval

fₘ= frequency of the modal class

f₁= frequency of the class previous to the modal class

f₂= frequency of the class subsequent to the modal class

**Solved Examples **

**Question- Find the mode of the data – 14, 16, 16, 16, 17, 16, 18 using the mean median mode formula. **

Answer- In the given data, there is only one value being repeated, it is a unimodal list.

Hence, mode = 16 according to the mean median mode formula.

**Question- The ages of the team members of a cricket team is as follows- **

**42, 38, 29, 37, 40, 33, 41 **

**Calculate the median of the given data using the mean median mode formula. **

Answer-

Arranging the given data in ascending order

29, 33, 37, 38, 40, 41, 42

Number of observations = 7 (odd)

Median = (7 + 1) ÷ 2ᵀᴴ term

= 4ᵀᴴ term

= 38

The median of the given data is 38