Mathematics 2013 JAMB Past Questions - Question 45: If the variance of 3+x,6,4,x and 7-x is 4 and the mean is 5,find the standard deviation .

Correct Answer

B

Explanation

let 82 and 8 denotes the variance and standard deviation of the distribution respectively.But 82 = 4 (given),hence, 8 = √4 = 2To find the standard deviation, we need to first calculate the variance and then take the square root of the variance.Given that the variance is 4 and the mean is 5, we can use the formula for variance:Variance = (sum of squared differences from the mean) / (number of data points)Let's calculate the sum of squared differences from the mean:(3+x - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (x - 5)^2 + (7 - x - 5)^2Simplifying this expression:(x - 2)^2 + 1^2 + (-1)^2 + (x - 5)^2 + (2 - x)^2Expanding and combining like terms:x^2 - 4x + 4 + 1 + 1 + x^2 - 10x + 25 + 4 - 4x + x^2Combining like terms:3x^2 - 18x + 35Now, we can set up the equation for variance:4 = (3x^2 - 18x + 35) / 5Multiplying both sides by 5:20 = 3x^2 - 18x + 35Rearranging the equation:3x^2 - 18x + 15 = 0Dividing both sides by 3:x^2 - 6x + 5 = 0Factoring the quadratic equation:(x - 5)(x - 1) = 0Setting each factor equal to zero:x - 5 = 0 or x - 1 = 0Solving for x:x = 5 or x = 1Now that we have the possible values of x, we can calculate the standard deviation. However, to do so, we need to know the specific value of x. If you provide the value of x (either 5 or 1), I can help you calculate the standard deviation.