Within & Overall Variation
Dhiresh Patil 
Within & Overall Variation
Dhiresh Patil
Overall variation refers to the total amount of variation or spread in a sample or population. It is a measure of the dispersion or spread of the data, and can be calculated using statistical measures such as the range, variance, or standard deviation.
Within variation, also known as within-group variation or within-subject variation, refers to the variation within a specific group or subgroup within a sample or population. It is a measure of the dispersion or spread of the data within a particular group or subgroup, and can also be calculated using statistical measures such as the variance or standard deviation.
Overall and within variation are important concepts in statistical analysis because they can help researchers to understand the dispersion or spread of the data and to identify patterns and trends in the data. They are often used in conjunction with measures of central tendency, such as the mean or median, to provide a more complete picture of the characteristics of a sample or population.
Overall and within variation can also be used to compare different groups or subgroups within a sample or population. For example, a researcher might compare the overall variation and within variation of different treatment groups in a medical study, or compare the overall variation and within variation of different demographic groups in a social science study.
Overall and within variation Explain with example
Overall variation and within variation are important concepts in statistical analysis that are used to measure the dispersion or spread of data in a sample or population. Here is an example to illustrate the difference between overall variation and within variation:
Imagine that a researcher is studying the height of a sample of 10 students in a high school. The heights of the students are measured in inches and are as follows:
Student 1: 64 inches Student 2: 68 inches Student 3: 60 inches Student 4: 63 inches Student 5: 71 inches Student 6: 65 inches Student 7: 67 inches Student 8: 62 inches Student 9: 69 inches Student 10: 66 inches
The overall variation in this sample can be calculated using a statistical measure such as the range, variance, or standard deviation. For example, the range of the heights is 71 inches - 60 inches = 11 inches, which represents the overall variation in the sample.
Now suppose that the researcher divides the students into two groups based on gender, with five male students and five female students. The heights of the male students are as follows:
Male Student 1: 64 inches Male Student 2: 68 inches Male Student 3: 60 inches Male Student 4: 63 inches Male Student 5: 71 inches
The heights of the female students are as follows:
Female Student 1: 65 inches Female Student 2: 67 inches Female Student 3: 62 inches Female Student 4: 69 inches
Overall and within variation Explain with example
Female Student 5: 66 inches
The within variation for the male students can be calculated using a statistical measure such as the variance or standard deviation. For example, the variance of the male student heights is (64-66.4)^2 + (68-66.4)^2 + (60-66.4)^2 + (63-66.4)^2 + (71-66.4)^2 = 17.76. This represents the within variation for the male students in the sample.
Similarly, the within variation for the female students can be calculated using a statistical measure such as the variance or standard deviation. For example, the variance of the female student heights is (65-66)^2 + (67-66)^2 + (62-66)^2 + (69-66)^2 + (66-66)^2 = 2. This represents the within variation for the female students in the sample.
Overall, overall variation and within variation are important concepts in statistical analysis that help researchers to understand the dispersion or spread of the data in a sample or population, and to identify patterns and trends in the data. In this example, the overall variation in the sample is 11 inches, while the within variation for the male students is 17.76 and the within variation for the female students is 2. These measures can be used to compare the dispersion of the data within and between the different groups in the sample.