Measurement of Central Tendency
CENTRAL TENDENCY
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Introduction
In statistics,
the central tendency is the descriptive summary of a data set. Through the
single value from the dataset, it reflects the Center of the data distribution.
Moreover, it does not provide information regarding individual data from the
dataset, where it gives a summary of the dataset. Generally, the central
tendency of a dataset can be defined using some of the measures in statistics.
Definition
The central
tendency is stated as the statistical measure that represents the single value
of the entire distribution or a dataset. It aims to provide an accurate
description of the entire data in the distribution.
Measures of
Central Tendency
The central tendency
of the dataset can be found out using the three important measures namely mean, median and mode.
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Mean
The mean
represents the average value of the dataset. It can be calculated as the sum of
all the values in the dataset divided by the number of values. In general, it
is considered as the arithmetic mean. Some other measures of mean used to find
the central tendency are as follows:
- Geometric
Mean
- Harmonic
Mean
- Weighted
Mean
It is observed
that if all the values in the dataset are the same, then all geometric,
arithmetic and harmonic mean values are the same. If there is variability in
the data, then the mean value differs. Calculating the mean value is completely
easy. The formula to calculate the mean value is given by:
Mean = (Sum
of all data points) ÷ (Number of data points)
OR
(X1 + X2
+ X3......Xn) /n
Median
Median is the
middle value of the dataset in which the dataset is arranged in the ascending
order or in descending order. When the dataset contains an even number of
values, then the median value of the dataset can be found by taking the mean of
the middle two values.
Consider the
given dataset with the odd number of observations arranged in descending order
– 23, 21, 18, 16, 15, 13, 12, 10, 9, 7, 6, 5, and 2
Here 12 is the
middle or median number that has 6 values above it and 6 values below it.
Now, consider
another example with an even number of observations that are arranged in
descending order – 40, 38, 35, 33, 32, 30, 29, 27, 26, 24, 23, 22, 19, and 17
When you look
at the given dataset, the two middle values obtained are 27 and 29.
Now, find out
the mean value for these two numbers.
i.e.,(27+29)/2
=28
Therefore, the
median for the given data distribution is 28.
Mode
The mode
represents the frequently occurring value in the dataset. Sometimes the dataset
may contain multiple modes and in some cases, it does not contain any mode at
all.
Consider the given
dataset 5, 4, 2, 3, 2, 1, 5, 4, 5
Since the mode
represents the most common value. Hence, the most frequently repeated value in
the given dataset is 5.
Based on the
properties of the data, the measures of central tendency are selected.
- If you have
a symmetrical distribution of continuous data, all the three measures of
central tendency hold good. But most of the times, the analyst uses the
mean because it involves all the values in the distribution or dataset.
- If you have
skewed distribution, the best measure of finding the central tendency is
the median.
- If you have
the original data, then both the median and mode are the best choice of
measuring the central tendency.
- If you have
categorical data, the mode is the best choice to find the central
tendency.
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