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Table of Content
The Mass/Concentration of the data is termed as the Central Tendency. It is a statistical measure that represents a value for the entire data.
Mean, Median, and Mode are the three measures that are used for calculating the Central Tendency.
The mean/average can be explained as the equal distribution of value to the total number of values. It is measured as the sum of the data points over the total number of values in the data.
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Median is the middle-most value of all the data points after sorting.
The mode is known to be the most frequently occurring value, commonly used for working on categorical data.
The biggest disadvantage is that the mean gets influenced by the outliers (also known as extreme values)
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Dispersion is the term used for the spread of data.
The measures used for the analysis of Dispersion of data are Variance, Standard Deviation, and Range.
The average of the squared distance of each data point from the center (mean) is defined as Variance.
In Variance, we calculate the square for distance, but along with the distance, the unit also gets squared, so to get back units we use Standard Deviation.
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Asymmetric of the distribution.
< +1 and > –1 a – Highly Skewed; Between –0.5 and –1 (or) +0.5 and +1 – Moderately Skewed; Between –0.5 and 0.5 – Approximately Symmetric.
Peakedness of the distribution. For Symmetric distributions, negative kurtosis implies a wider peak and thinner tails. For Symmetric distributions, positive kurtosis implies a narrow peak and wider tails.
Kurtosis is a measure of the spread of the data from the centre. It is the 4th business moment which speaks about the shape of the distribution as being high peaked or wide peaked.
Kurtosis is calculated as the average distance of the data points from the centre.
∑_(i=1)^n [((x-μ)/σ)]4 - 3
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Skewness is a measure that represents the mass of the data distributed towards the right side of the center. A histogram on the data will also enable us to understand the existence of extreme value in the dataset.
Skewness is a measure that represents the mass of the data distributed towards the left side of the center. A histogram on the data will also enable us to understand the existence of extreme value in the dataset.
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The Mean is calculated as the sum of the data points over the total number. The sum gets altered with a change in any single value in the data.
Median and Mode measures do not get affected by this change.
The mean of the data is influenced by extreme values, whereas the median won't. Skewness in the data distribution is an effect of this extreme value. If the data is positively skewed that means the mean is pulled towards that positive side. Hence Mean is greater than the Median for such data. So we can conclude Mean > 50.
The squared distance from the Mean to each data point is used in calculating the Standard Deviation. As we are squaring the values, we cannot get a negative value.
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The distance of the data points from the center would be affected by outliers. Yes, the Standard Deviation would get effected.
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