Measures of Central tendency:
Mean: airthmetic average of the overall dataset
Median: middle value of the dataset when it is arranged in ascending order
its the middle value if the dataset is odd, and average of the two middle values if the dataset is even
Suppose the height of the trees (metres) in a garden is represented by following dataset
1,2,3,4,6,7,4,2,3,8,9,1,2
first let us arrange this in ascending order
1,1,2,2,2,3,3,4,4,6,7,8,9
most frequent value in dataset in here is "2" = Mode
now the total no. of values in the datset is 13
Median will be value that is middle value that is 7th one
Median =3
Mean = (1+1+2+2+2+3+3+4+4+6+7+8+9)/13
= 4
Mean: airthmetic average of the overall dataset
Properties:
1. Uniqueness: for a given set of data, there is only one arithmetic mean
2. Simplicity: easy to compute
3. Extreme values have drastic influence on mean
Median: middle value of the dataset when it is arranged in ascending order
its the middle value if the dataset is odd, and average of the two middle values if the dataset is even
it is the value that divides the dataset into two equal parts such that the no. of values equal to or greater than the median is equal to the number of values equal to or less than the median, when the data set is arranged in order of magnitude
In odd data set: it is the (n+1)/2 th value
In even data set: it is the average of n/2 and n/2+1 th value
Properties:
1. Uniqueness: for a given set of data, there is only one median
2. Simplicity: easy to compute
3. Not drastically affected by extreme values as in mean
Mean and median are special cases of a family of parameters known as location parameters, because they can be used to designate certain positions on the horizontal axis when the distribution of a variable is graphed (“locate” the distribution on the horizontal axis)
Mode: most frequent value in the dataset
It may be used also for describing qualitative data.
Suppose the height of the trees (metres) in a garden is represented by following dataset
1,2,3,4,6,7,4,2,3,8,9,1,2
first let us arrange this in ascending order
1,1,2,2,2,3,3,4,4,6,7,8,9
most frequent value in dataset in here is "2" = Mode
now the total no. of values in the datset is 13
Median will be value that is middle value that is 7th one
Median =3
Mean = (1+1+2+2+2+3+3+4+4+6+7+8+9)/13
= 4
PSM / COMMUNITY MEDICINE by Dr Abhishek Jaiswal is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at learnpsm@blogspot.com.
Permissions beyond the scope of this license may be available at jaiswal.fph@gmail.com.
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