The median of a set of 8 consecutive even integers is 61. What is the largest integer in the set?
If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
54,56,58,60,62,64,66,68
Thanks Sir
To find the largest integer in the set, we need to determine the first integer in the set. Since we're given that the set consists of consecutive even integers, we can use the concept of median here.
The median of a set of numbers is the middle value when the numbers are arranged in ascending order. If we have 8 consecutive even integers, the median will be the 4th number.
We know that the median is given as 61, so we need to determine the first integer in the set.
Let's denote the first integer as 'x'. Since the set consists of consecutive even integers, the second integer will be 'x + 2', the third integer will be 'x + 4', and so on.
To find the median, we need to determine the 4th number. Since the median is 61, the 4th number is 'x + 6'.
Since the set has 8 consecutive even integers, the 4th number should be the middle value.
Therefore, we can set up the equation:
x + 6 = 61
Solving this equation, we find:
x = 61 - 6
x = 55
So, the first integer in the set is 55.
To find the largest integer, we can add 6 to 55 (since the numbers are consecutive even integers):
55 + 6 = 61
Therefore, the largest integer in the set is 61.