Lindsey found the median and mean of the list of numbers below.
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.
D.
The mean would decrease.
C.
The mean would increase.
To determine whether the median and mean would increase or decrease when the number 23 is included in the list, let's calculate the median and mean for both scenarios.
Without 23:
Arranging the numbers in ascending order: 4, 6, 8, 8, 15
Median = (8 + 8) / 2 = 8
Mean = (4 + 6 + 8 + 8 + 15) / 5 = 41 / 5 = 8.2
With 23 included:
Arranging the numbers in ascending order: 4, 6, 8, 8, 15, 23
Median = (8 + 8) / 2 = 8
Mean = (4 + 6 + 8 + 8 + 15 + 23) / 6 = 64 / 6 = 10.67
From the calculations above, we can see that the median remains the same (8) regardless of whether the number 23 is included. However, the mean increases from 8.2 to 10.67 when the number 23 is included.
Therefore, the correct statement is:
C. The mean would increase.
To find the median, Lindsey simply needs to arrange the numbers in ascending order and then find the middle value. To find the mean, Lindsey needs to sum up all the numbers in the list and divide by the total number of values.
Let's first find the median and mean of the given list: 4, 6, 8, 8, 15.
Median: Arranging the numbers in ascending order, we get 4, 6, 8, 8, 15. The middle value is 8, so the median is 8.
Mean: Summing up all the numbers, we get 4 + 6 + 8 + 8 + 15 = 41. Dividing by the total number of values (5), we get 41/5 = 8.2. So the mean is 8.2.
Now, let's look at what happens when we include the number 23 in the list.
If we add 23 to the list (4, 6, 8, 8, 15, 23):
The median would increase: As the list is now longer and includes a larger value (23), the median would shift to a higher value. In this case, the median would become 8, since it's the middle value when arranged in ascending order.
The mean would increase: Adding a larger value (23) to the list would increase the sum of all the numbers when computing the mean. Since the new sum is higher, dividing by the total number of values would result in a higher mean value. In this case, the mean would become (41+23)/6 = 10.67.
Therefore, the correct statement is:
C. The mean would increase.