A statistics student collects data for a project and determines the variance of his data set to be 49. If he represents the variance as a difference of squares, what are the two numbers he can use?
Answer
Step 2: Recall that the formula for factoring a difference of squares is \(a^2 - b^2 = (a - b)(a + b)\). Therefore, the two numbers we are looking for are the standard deviation and its negation, 7 and -7.
Step 1 ：Step 1: Recall that the variance is a square quantity, so its square root will give us the standard deviation. Therefore, take the square root of the variance to find the standard deviation: \( \sqrt{49} = 7 \)
Step 2 ：Step 2: Recall that the formula for factoring a difference of squares is \(a^2 - b^2 = (a - b)(a + b)\). Therefore, the two numbers we are looking for are the standard deviation and its negation, 7 and -7.
