Numerical Application

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Average (Mean) = Sum of all observations / Total number of observations Average represents a calculated central value of given data and is a measure of central tendency. It lies between the maximum a

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Weighted average considers that some elements carry more weight than others. Weighted Average (x̄w) = Σⁿᵢ₌₁ wᵢxᵢ / Σⁿᵢ₌₁ wᵢ where wᵢ = weight of iᵗʰ element, xᵢ = value of iᵗʰ element Example: Grad

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Average Speed = Total distance travelled / Total time taken (direction independent) Average Velocity = Total displacement / Total time taken (direction dependent) Key difference: Average speed canno

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Odd Days = Extra days left after exact number of weeks For example: 31 days = 4 weeks + 3 days, so 3 odd days Ordinary year = 365 days = 52 weeks + 1 day → 1 odd day Leap year = 366 days = 52 weeks

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Hour Hand Speed = 30° per hour = 0.5° per minute Minute Hand Speed = 360° per hour = 6° per minute The minute hand is 12 times faster than the hour hand.

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22 times in a day They coincide every 12/11 hours = 65 5/11 minutes ≈ 65.45 minutes They don't coincide between 11 o'clock to 12 o'clock (this happens twice in 24 hours), so 24 - 2 = 22 times.

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A = |30H + m/2 - 6m| = |30H - 11m/2| where H = hours, m = minutes Alternatively: T = (2/11)(H × 30° ± A) where T = time in minutes, A = angle between hands

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A year is a leap year if: 1. It is divisible by 4 2. For century years (ending in 00), it must be divisible by 400 Examples: 2020 is leap year (divisible by 4) 2000 is leap year (divisible by 400) 19