Applications of Permutation and Combination

Applications of Permutation and Combination Functional Applications (i) The number of all permutations (arrangements) of n different objects taken r at a time, When a particular object is to be always included in each arrangement is n-1Cr-1 x r! When a particular object is never taken in each arrangement is n-1Cr x r! (ii) If Read more about Applications of Permutation and Combination[…]

Applications of De-Moivre’s Theorem

De-Moivre’s Theorem: A simple formula for calculating powers of complex numbers in the form of cosθ and sinθ is known as de-Moivre’s theorem. If n is a rational number, then (cosθ + sinθ)ⁿ = cos nθ + i sin nθ. Applications of De-Moivre’s Theorem: If z = (cosθ₁ + i sinθ₁) (cosθ₂ + i sinθ₂) … Read more about Applications of De-Moivre’s Theorem[…]

Variance and Standard Deviation of Ungrouped Data

Variance and Standard Deviation of Ungrouped Data Formulas: The variance is . Then ‘σ’ the standard deviation is given by the positive square root of the variance . Calculation of Variance and Standard Deviation for an Ungrouped Data 1. Find the variance and standard deviation of following data 5, 12, 3, 18, 6, 8, 2, Read more about Variance and Standard Deviation of Ungrouped Data[…]

Mean Deviation about the Median and Mean Deviation from the Mean

Mean Deviation about the Median and Mean Deviation from the Mean   Mean Deviation about the Median: To find the mean deviation about the median we have to find the median of the given discrete frequency distribution. After arranging the observations in either ascending order, we shall find the sum of the frequency ∑fᵢ = Read more about Mean Deviation about the Median and Mean Deviation from the Mean[…]