Determine all possible values of the integer m such that the median and mean of the five integers 3, 6, 9, 11 and m are the same.
If m is in the middle, 3 6 m 9 11
then m can be any of 6,7,8,9
For those values, the mean is 7, 7.2, 7.4, 7.6, 7.8
so, m cannot be in the middle.
Now you try other positions and possible results. It's not hard; just be careful.
m=1,16? Thanks
To find the possible values of integer m such that the median and mean of the five integers 3, 6, 9, 11, and m are the same, we first need to understand what the median and mean are.
1. Median: The median is the middle value when the numbers are arranged in ascending order. If there are an odd number of integers, the median is the middle number. If there are an even number of integers, the median is the average of the two middle numbers.
2. Mean: The mean is obtained by adding up all the numbers and dividing by the total count of numbers.
Now let's find the median and mean values for the given numbers:
Arranging the numbers in ascending order: 3, 6, 9, 11, and m.
1. Median:
As there are 5 numbers, the median will be the middle number. In this case, the middle number is 9.
2. Mean:
To find the mean, we need to add up all the numbers and divide by the count. The sum of the given numbers is 3 + 6 + 9 + 11 + m = 29 + m. Since there are 5 numbers, the mean is (29 + m) / 5.
To find the possible values of m for which the median and mean are the same, we equate the median and mean:
9 = (29 + m) / 5
Multiplying both sides of the equation by 5:
45 = 29 + m
Subtracting 29 from both sides:
16 = m
So the only possible value for integer m is 16, where the median and mean of the numbers 3, 6, 9, 11, and 16 are both equal to 9.