Mean, Median and Mode
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' = For Eg: Find the mean of 4,6,8,6,7,8
Sol:Mean X' = = (4 + 6 + 8 + 6 + 7 + 8)/6= 39/6= 6.5
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 th observation in the arrangement of observations in increaseing 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
For Eg: Find the median of the following observations
Sol: Observations in the ascending order are :
4, 6, 6, 7, 8, 8, 8
Here, n = 7 is odd.
M = Value of (n+1)/2 th observation
= Value of (7+1)/2 th observation
= Value of 4 th observation
Mode of ungrouped data:An observation occurring most frequently in the data is called mode of the data. It is denoted by Z.
For Eg:Find the mode of the following observations
In the given data, the observation 8 occurs maximum
number of times (3)
Mode(Z) = 8