Exercise 47 Page 60

We are asked to write a set of five different integers that has a mean of -10. To do so, let's recall the definition of the mean of a data set.

Let's imagine that we want to find the mean of a data set 3, 4, 5, 6. To do so, we add these numbers and divide the sum by 4, because we have 4 values. Mean: 3+4+5+6/4 = 18/4 = 4.5 Now, we want to write a set of five different integers that has a mean of -10. Because we already know that there must be 5 integers in our data set, we will have 5 in the denominator in the formula for the mean. We want the mean to be equal to -10 ?/5 = -10 Now, we need to find 5 different integers whose sum divided by 5 will give us -10. To do so, let's begin by taking 4 different integers, for example 1, 2, 3, 4. We will call the fifth one x. 1+2+3+4+x/5 = -10 Let's solve the above equation for x.

We found that x= -60. This means that the mean of 1, 2, 3, 4, and -60 is -50. We found a set of five different integers that has a mean of -10. Note that we could take any different four integers and then, we would find a different value of the fifth integer x.