Hi I’m having trouble with this math topic How changing a value affects the mean and median. My math problem is The monthly rent (in dollars) paid by 10 people are given below. The numbers are 795, 935, 960, 995, 1025, 1030, 1050, 1090, 1105
For the mean, add them up , then divide by 9
For the median, list them in order, the median is the number in the middle.
I’m sorry but I’ve got another question about the pre algebra..
The numbers of trading cards owned by eight middle school students are given: 293, 378, 441, 458, 482, 485, 529, 614
Suppose that the number 614 from this list changes to 486
What happens to the median? What happens to the mean?
The median now is (458+482)/2
If 614 changes to 486, the median stays the same, since 486 is still higher than the median
Bu the mean will be less, because the sum of the numbers will be less.
To understand how changing a value affects the mean and median, let's first define what the mean and median are:
1. Mean: The mean is the average of a set of numbers. To find the mean, you sum up all the numbers and divide the sum by the total count of numbers.
2. Median: The median is the middle value of a set of numbers when they are arranged in order. If there are an even number of values, the median is the average of the two middle values.
Now, let's calculate the mean and median for the given set of rent values (795, 935, 960, 995, 1025, 1030, 1050, 1090, 1105):
Step 1: Sort the numbers in ascending order:
795, 935, 960, 995, 1025, 1030, 1050, 1090, 1105
Step 2: Calculate the mean:
To find the mean, we sum up all the numbers:
795 + 935 + 960 + 995 + 1025 + 1030 + 1050 + 1090 + 1105 = 9075
Then, we divide the sum by the total count of numbers (which is 9 in this case):
9075 / 9 = 1008.33 (rounded to two decimal places)
So, the mean rent is approximately $1008.33.
Step 3: Calculate the median:
Since there are 9 numbers, the median will be the middle value in the sorted list.
The middle value is the 5th value, which is 1025.
So, the median rent is $1025.
Now, let's see how changing a value can affect the mean and median:
For example, if we change the highest rent value from 1105 to 1205:
New set of rent values: 795, 935, 960, 995, 1025, 1030, 1050, 1090, 1205
Step 1: Sort the numbers in ascending order:
795, 935, 960, 995, 1025, 1030, 1050, 1090, 1205
Step 2: Calculate the mean:
Sum of numbers = 795 + 935 + 960 + 995 + 1025 + 1030 + 1050 + 1090 + 1205 = 9085
Total count of numbers = 9
Mean = Sum of numbers / Total count of numbers = 9085 / 9 = 1009.44 (rounded to two decimal places)
So, the new mean rent is approximately $1009.44.
Step 3: Calculate the median:
Since there are 9 numbers, the median will be the middle value in the sorted list.
The middle value is still the 5th value, which is 1025.
So, the new median rent is still $1025.
From this example, we can observe that changing a single value affects the mean, but it does not affect the median as long as the value is not the new middle value. The median only changes when the value being replaced is the current median.
I hope this helps clarify how changing a value can affect the mean and median! Let me know if you have any further questions.