# Mean, Median and Mode of Ungrouped Data

Mean, median, mode of ungrouped data:

Ungrouped Data (Raw Data): The information collected systematically regarding a population or a sample survey is called an ungrouped data. It is also called raw data.

Mean of ungrouped data:

Let x1, x2, x3, ..., xn be n observations then mean is obtained by dividing the sum of n observations by n. It is denoted by

X' = åXi/n

Demonstration:

Find the mean of 8,12,16,12,14,8

Solution :

Mean X' = åXi/n
= (8+12+16+12+14+8) / 6
70/6
= 11.66

Median of ungrouped data:

If the observations of an ungrouped data are arranged in increasing or decreasing order of their magnitude+ a value which divides these ordered observations into two equal parts is called the median of the data. It is denoted by M.

If the number of observations (n) is an odd integer+ then
M = Value of (n+1)/2 the observation in the arrangement of observations in increasing order.

If the number of observations (n) is an even integer+ then
M = (Value of n/2 th observation + Value of (n/2 + 1) th observation)/2

Demonstration:

Find the median of the following observations
4+6+8+6+7+8+8

Solution:

Observations in the ascending order are :
4+ 6+ 6+ 7+ 8+ 8+ 8
Here+ n = 7 is odd.

Median :

M = Value of (n+1)/2 th observation
= Value of (7+1)/2 th observation
= Value of 4 th observation
= 7

Mode of ungrouped data:
An observation occurring most frequently in the data is called mode of the data. It is denoted by Z.

Demonstration:

Find the median of the following observations
4+6+8+6+7+8+8

Solution:

In the given data 8 occurs maximum
number of times (3)
Mode(Z) = 8