Question

dig deeper complete the list of five different integers so that they have a mean of -10. explain how you found your answer. -10, 0, □, -5, -15 the □ of the integers needs to be □ so that when it is divided by □ the quotient is -10.

Explanation:

Step1: Recall the mean formula

The mean of a set of numbers is given by the sum of the numbers divided by the count of numbers. Let the missing integer be \( x \). The set of integers is \(-10, 0, x, -5, -15\) and the mean is \(-10\). The formula for the mean \(\bar{x}\) is \(\bar{x}=\frac{\text{Sum of numbers}}{\text{Number of numbers}}\). Here, \(\bar{x} = - 10\) and the number of numbers \(n = 5\). So we have the equation \(-10=\frac{-10 + 0+x-5 - 15}{5}\).

Step2: Simplify the numerator

First, simplify the numerator of the fraction: \(-10+0 - 5-15=-30\). So the equation becomes \(-10=\frac{-30 + x}{5}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(5\) to get rid of the denominator: \(-10\times5=-30 + x\), which simplifies to \(-50=-30 + x\). Then add \(30\) to both sides: \(x=-50 + 30=-20\).

Answer:

The missing integer is \(-20\). The sum of the integers needs to be \(-50\) (since mean \(\times\) number of integers \(=-10\times5 = - 50\)) so that when it is divided by \(5\) (the number of integers), the quotient is \(-10\). The completed list is \(-10, 0, -20, -5, -15\).