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[…]
Applications of Binomial Theorem (i) R-F Factor Relation: Here, we are going to discuss problems involving (√A + B)ⁿ = I + f, where I and n are positive integers. 0 ≤ f ≤ 1, |A – B²|= k and |√A+B|< 1. Approach for these types of problems can be learnt from following examples. Example: Read more about Applications of Binomial Theorem[…]
Intermediate Value Theorem Suppose that f(x) is continuous on [a, b] and let M be any number between f (a) and f (b). Then there exists a number C such that. a < c < b f (c) = M All the intermediate value theorem is really saying is that a continuous functions will take Read more about Intermediate Value Theorem[…]
Squeeze Principle Assume that function f.g and h satisfy g(x) ≤ f (x) ≤ h (x) and then . Note: The quantity a may be a finite number +∞ or -∞. The quantity L may be finite number +∞ or -∞. The squeeze principle is used on limit problems where the useful algebraic methods (factoring conjugation, Read more about Squeeze Principle[…]
Mean Deviation for Grouped Data Mean Deviation about the Mean: Recall the arithmetic mean (x̄) of a discrete frequency distribution with n data points is obtained using the formula: x̄ = (ⁿ∑i=₁ xi fi)/ ⁿ∑i=₁ fi = (ⁿ∑i=₁ xi fi)/ N. Where, N = ⁿ∑i=₁ fi Now the mean deviation about the mean i.e., M.D Read more about Mean Deviation for Grouped Data[…]
Mean Deviation from the Mean for UnGrouped Data Suppose we have a discrete data with n observations x₁, x₂, … xn. Then we adopt the following procedure for computing the mean deviation from the mean of the given data. Step 1: Calculate the arithmetic mean (x̄) of the n observations. Let it be “a”. Step Read more about Mean Deviation from the Mean for UnGrouped Data[…]
Trigonometric Ratios & Identities – Problems 1) Find the value of i) sin (5π/4) ii) tan (855°) iii) tan [-23 π/3] iv) sec (13 π/3) Solutions: i) Given that sin (5π/4) = sin [2π – (π/3)] (since sin (180 – x) = – sinx) = – sin (π/3) = (√3/2) ii) Given that tan (855°) Read more about Trigonometric Ratios & Identities – Problems[…]
Division Algorithm If 0 ≠ a, b ϵ Z then ∃ q, r ϵ Z uniquely such that b = aq + r where 0 ≤ r < |a|. A nonzero integer a is said to divide an integer b if there exist q ϵ z such that b = aq. It is denoted by Read more about Division Algorithm[…]
Inverse of the Function – Problems 1. The inverse of the function is Solution: , ⇒ x = ½ log₁₀ , Let y = f (x) ⇒ x = f⁻¹ (y) ⇒ f⁻¹ (y) = ½ log₁₀ , ⇒ f⁻¹ (x) = ½ log₁₀ . 2. If f: R → R is defined by f Read more about Inverse of the Function – Problems[…]
Functions (Range) – Problems 1. The range of the function =? Solution: , , ∴ Range of f (x) is {-1, 1}. 2. If x is real then value of the expression lies between ? Solution: , Let us y = . ⇒ x² + 14x + 9 = yx² + 2xy + 3y ⇒ Read more about Functions (Range) – Problems[…]