Statistics

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Ungrouped data: Raw data where individual values are listed separately. Example: Marks of students - 76, 82, 64, 53, 90, etc. Grouped data: Data organized into class intervals or groups. Example: Mar

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Mean (x̄) = Σfixi / Σfi Where: - xi = individual observations - fi = frequency of each observation - Σ = summation symbol This formula is used when data values have different frequencies.

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Class mark is the mid-point of a class interval that represents all observations in that class. Formula: Class mark = (Upper class limit + Lower class limit) / 2 Example: For class 10-25, class mark

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Direct Method: x̄ = Σfixi / Σfi Where: - xi = class marks - fi = frequency of each class - This is the same formula as ungrouped data but uses class marks instead of individual values

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Assumed Mean Method: x̄ = a + (Σfidi / Σfi) Where: - a = assumed mean (any chosen xi) - di = xi - a (deviation from assumed mean) - Used when xi values are large to simplify calculations - Choose 'a'

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Step-Deviation Method: x̄ = a + h(Σfiui / Σfi) Where: - a = assumed mean - h = class interval size (or common factor of di values) - ui = (xi - a) / h - Used when di values have a common factor to fu

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Mode is the value that occurs most frequently in a dataset. For ungrouped data: 1. Arrange data in ascending order 2. Count frequency of each value 3. The value with highest frequency is the mode Ex

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Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] × h Where: - l = lower boundary of modal class - f1 = frequency of modal class - f0 = frequency of class preceding modal class - f2 = frequency of class succe