Statistics

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Mean = x̄ = (Σxᵢfᵢ)/N, where xᵢ is the class mark, fᵢ is the frequency of each class, and N is the total number of observations (Σfᵢ).

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Class mark (xᵢ) = (Lower class limit + Upper class limit)/2. For example, for class 20-24, class mark = (20+24)/2 = 22.

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Assumed mean method uses the formula x̄ = A + d̄, where A is any assumed mean and d̄ is the mean of deviations. It reduces calculations when dealing with large numbers by working with smaller deviatio…

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x̄ = A + ūg, where A = assumed mean, ū = mean of step deviations (uᵢ), g = common factor (GCD of all deviations), and uᵢ = dᵢ/g where dᵢ = xᵢ - A.

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Step deviation method is chosen when the class marks are large numbers and have a common factor (GCD). It simplifies calculations by converting large numbers into smaller, manageable values.

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Median is the middle value that divides data into two equal parts. Unlike mean (which can be affected by extreme values), median represents the central position and is not influenced by very high or v…

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Median = L + [(N/2 - CF)/f] × h, where L = lower limit of median class, N = total frequency, CF = cumulative frequency before median class, f = frequency of median class, h = class interval.

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Find N/2 (where N is total frequency). The median class is the class whose cumulative frequency is just greater than or equal to N/2. This class contains the median value.