MATHEMATICS

JAMB 2000 - Question 47

Mathematics 2000 JAMB Past Questions - Question 47: The variance of x,2x,3x,4x, and 5x is

The variance of x,2x,3x,4x, and 5x is
The variance of x,2x,3x,4x, and 5x is
A:
B:
C:
D:
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Correct Answer

B

Explanation

check solution in the diagram above To find the variance of a set of numbers, we need to follow these steps:1. Calculate the mean (average) of the numbers.2. Subtract the mean from each number and square the result.3. Calculate the mean of the squared differences.Let's apply these steps to the given set of numbers: x, 2x, 3x, 4x, and 5x.Step 1: Calculate the mean:Mean = (x + 2x + 3x + 4x + 5x) / 5 = 15x / 5 = 3xStep 2: Subtract the mean from each number and square the result:(x - 3x)^2 = (-2x)^2 = 4x^2(2x - 3x)^2 = (-x)^2 = x^2(3x - 3x)^2 = 0^2 = 0(4x - 3x)^2 = x^2(5x - 3x)^2 = 2x^2Step 3: Calculate the mean of the squared differences:Mean of squared differences = (4x^2 + x^2 + 0 + x^2 + 2x^2) / 5                          = (8x^2) / 5                          = 8x^2 / 5Therefore, the variance of the numbers x, 2x, 3x, 4x, and 5x is 8x^2 / 5.