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Median
The median of a set of data values is the middle value of the data set when it has been arranged in ascending order. That is, from the smallest value to the highest value Median is calculated as
Where n is the number of values in the data
If the number of values in the data set is even, then the median is the average of the two middle values.
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Mode
Mode of a statistical data is the value of that variable which has the maximum frequency
S.no | Term | Description |
1 | Mean for Ungroup Frequency table | Mean is given by |
2 | Mean for group Frequency table | In these distribution, it is assumed that frequency of each class interval is centered around its mid-point i.e. class marks Class mark Mean can be calculated using three method a) Direct method b) Assumed mean method Where Assumed mean c) Step deviation Method Where a= Assumed mean |
3 | Mode for frequency table | Modal class: The class interval having highest frequency is called the modal class and Mode is obtained using the modal grouped class Where I = lower limit of the modal class, h = size of the class interval (assuming all class sizes to be equal), = frequency of the modal class, = frequency of the class preceding the modal class, = frequency of the class succeeding the modal class. |
4 | Median of a grouped data frequency table | For the given data, we need to have class interval, frequency distribution and cumulative frequency distribution Median is calculated as Where l= lower limit of median class, n = number of observations, cf = cumulative frequency of class preceding the median class, f = frequency of median class, h = class size (assuming class size to be equal) |
5 | Empirical Formula between Mode, Mean and Median | 3 Median =Mode + 2 Mean |