Mean and Median

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The mean (also called arithmetic mean or average) is the sum of all observations divided by the total number of observations. Formula: x̄ = (x₁ + x₂ + x₃ + ... + xₙ)/n = (1/n)∑xᵢ where x̄ is the mean,

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Step 1: Add all observations: 12 + 15 + 18 + 20 + 25 = 90 Step 2: Count total observations: n = 5 Step 3: Calculate mean: x̄ = 90/5 = 18 Therefore, the mean is 18.

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∑xᵢ (sigma notation) represents the sum of all observations from i=1 to n. For example, ∑x₁ to x₅ = x₁ + x₂ + x₃ + x₄ + x₅. It's a mathematical shorthand for adding all values in a dataset.

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Property 1: If x̄ is the mean of n observations, then the sum of deviations of all observations from their mean is zero. Mathematically: ∑(x - x̄) = 0. This means the positive and negative deviations

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Given: Mean = 10, n = 5 Using formula: (5 + 8 + 12 + x + 15)/5 = 10 (40 + x)/5 = 10 40 + x = 50 x = 50 - 40 = 10 Therefore, x = 10.

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Property 2: If each observation is increased by a constant 'a', then the new mean = old mean + a. So if each observation is increased by 5, the new mean = original mean + 5. Example: If original mean

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Property 4: If each observation is multiplied by a constant 'a', then the new mean = a × old mean. So if each observation is multiplied by 3, the new mean = 3 × original mean. Example: If original mea

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Median is the middle value of a dataset when arranged in ascending or descending order. Steps: 1) Arrange data in order 2) Count total observations (n) 3) If n is odd: median = ((n+1)/2)th term 4) If