Lindsey found the median and mean of the list of numbers below.

Question

4, 6, 8, 8, 15

Which statement is true if Lindsey includes the number 23 in the list?

A.
The median would decrease.

B.
The median would increase.

C.
The mean would increase.

Answer 1

Let's analyze the original list of numbers first:

Original list: 4, 6, 8, 8, 15

1. Finding the median: The median is the middle value in a sorted list. Since there are 5 numbers in the list, the median is the third number:

   • Median = 8

2. Finding the mean: Mean is calculated as the sum of the numbers divided by the count of numbers.

   • Sum = 4 + 6 + 8 + 8 + 15 = 41
   • Mean = 41 / 5 = 8.2

Now, let's include the number 23 in the list:

New list: 4, 6, 8, 8, 15, 23

1. Finding the new median: The new list has 6 numbers, so the median is the average of the 3rd and 4th numbers:

   • New list in order: 4, 6, 8, 8, 15, 23
   • The 3rd number is 8, and the 4th number is also 8.
   • Median = (8 + 8) / 2 = 8

   So the median remains 8.

2. Finding the new mean:

   • New Sum = 4 + 6 + 8 + 8 + 15 + 23 = 64
   • New Mean = 64 / 6 = 10.67

Now, let's analyze the statements:

A. The median would decrease.

• False: The median remains the same at 8.

B. The median would increase.

• False: The median remains the same at 8.

C. The mean would increase.

• True: The mean changed from 8.2 to approximately 10.67, so it increased.

Therefore, the correct statement is:

C. The mean would increase.