Question

The median of a set of eight numbers is 4.5. Given that seven of the numbers are 7, 2, 13, 4, 8, 2, and 1, find the eighth number and write down the mode of the eight numbers.

a) Eighth number: 4, Mode: 2

b) Eighth number: 5, Mode: 2

c) Eighth number: 4, Mode: 4

d) Eighth number: 5, Mode: 4

Answer 1

The eighth number is 5, making the ordered list complete, and the mode of all eight numbers is 2, as it is the number that appears most frequently among them.

Step-by-step explanation:

To find the eighth number in a set of eight numbers having a median of 4.5, we must first arrange the seven given numbers in ascending order: 1, 2, 2, 4, 7, 8, 13. Since we have eight numbers in total, the median will be the average of the fourth and fifth numbers in this ordered list. Since the known median is 4.5, the unknown eighth number (x) must be such that (4 + x) / 2 = 4.5, which implies that x = 5. Therefore, the eighth number is 5. After including this eighth number, the ordered list is: 1, 2, 2, 4, 5, 7, 8, 13. We can now determine the mode of the numbers, which is the value that appears most frequently. Since 2 appears twice and no other number does, the mode is 2.