the median of a set of six number is 2.5
given that five number are 8, 1 , 2 , 11 and 1 , find the sixth number .
and explain ...
arrange them in order:
1,1,2,x,8,11
now x must be bigger than 2 and smaller than 8
There will be an even number of numbers, 6, so the median will be the mean of the two center ones, 2 and x
well
(2+x)/2 = 2.5
2+x = 5
x = 3
To find the sixth number, we need to determine the value that will make the median of the set equal to 2.5.
To begin, let's arrange the five given numbers in ascending order: 1, 1, 2, 8, 11.
Since the median is the middle value of a set when arranged in order, we can see that the median will be either 2 or 8.
Since the median is given to be 2.5, we can conclude that the sixth number must be larger than 2 but smaller than 8. Specifically, it must be in the range of 2 to 8.
Without further information, we cannot determine the exact value of the sixth number. It could be any value between 2 and 8, as long as the median of the complete set is 2.5.
To find the sixth number in the set, we can use the information given that the median of the set is 2.5. The median is the middle value when the numbers are arranged in ascending order. Since we have five numbers given, we need to determine the sixth number.
First, let's arrange the given numbers in ascending order: 1, 1, 2, 8, 11.
The median of this set is the value in the middle, which is 2. To confirm this, count the number of values in the set. Since we have five numbers, the middle value is the third number, which is indeed 2.
Now, we know that the median of the original set is 2.5, but we already have a set of five numbers with a median of 2.
To find the sixth number, we need to introduce another number that is larger than the existing numbers but still smaller than the next larger value in the set, which is 8.
Therefore, the sixth number in the set is any value between 2 and 8. Since we don't have any additional information, there are several possible values that could be the sixth number, such as 3, 4, 5, 6, or 7.