Best Video on MEASURES OF DISPERSION || part-11|| Research Methodology

Hi guys! This is the 11th part of research methodology playlist,where I have discussed Measures of Dispersion and its types ,which is a part of ugc net unit-2 syllabus AND it will help you in your first paper also ,so watch full playlist.
Hope so that it will help you in your CUET-PG and NET/JRF preparation .

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Measures of dispersion, also known as measures of variability, are statistical tools that describe the spread or variability of data within a dataset. They give us an idea of how much the data points differ from each other and from the mean. Here are the key measures of dispersion:

1. Range:
• The simplest measure of dispersion.
• It is the difference between the maximum and minimum values in a dataset.
• Formula: Range = Maximum Value - Minimum Value
2. Interquartile Range (IQR):
• Measures the spread of the middle 50% of the data.
• It is the difference between the third quartile (Q3) and the first quartile (Q1).
• Formula: IQR = Q3 - Q1
3. Variance:
• Measures the average squared deviation of each data point from the mean.
• It gives an indication of how much the data points differ from the mean.
• Formula:
• For a sample: S^2 = \frac{\sum{(X_i - \bar{X})^2}}{n-1}
• For a population: \sigma^2 = \frac{\sum{(X_i - \mu)^2}}{N}
• Here, X_i is each individual data point, \bar{X} is the sample mean, \mu is the population mean, n is the sample size, and N is the population size.
4. Standard Deviation:
• The square root of the variance.
• It is more interpretable than variance as it is in the same units as the data.
• Formula:
• For a sample: S = \sqrt{\frac{\sum{(X_i - \bar{X})^2}}{n-1}}
• For a population: \sigma = \sqrt{\frac{\sum{(X_i - \mu)^2}}{N}}
5. Mean Absolute Deviation (MAD):
• Measures the average absolute deviation of each data point from the mean.
• It is less sensitive to outliers compared to variance and standard deviation.
• Formula: MAD = \frac{\sum{|X_i - \bar{X}|}}{n}
6. Coefficient of Variation (CV):
• Expresses the standard deviation as a percentage of the mean.
• It is useful for comparing the degree of variation between datasets with different units or means.
• Formula: CV = \frac{S}{\bar{X}} \times 100

These measures help in understanding the spread and consistency of the data, which is essential in many statistical analyses.