There are 9 observation in a set of data Arranged in size. the sum of the first 5 is 26,the sum of the last 5 is 34,and the mean of all is 9 and 6. Find the median of the set? ?

To find the median of the set, we first need to determine the total sum of all 9 observations.

Let the observations be denoted as a1, a2, a3, a4, a5, a6, a7, a8, a9.

Given:
Sum of the first 5 observations = a1 + a2 + a3 + a4 + a5 = 26
Sum of the last 5 observations = a5 + a6 + a7 + a8 + a9 = 34
Mean of all observations = (a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9) / 9 = 9 and 6

From the mean, we can calculate the total sum of all observations:
(a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9) = 9 and 6 * 9 = 87

Now, we can substitute the given sums of the first 5 and last 5 observations into the total sum equation:
26 + a6 + a7 + a8 + a9 = 87
a6 + a7 + a8 + a9 = 87 - 26 = 61

34 + a1 + a2 + a3 + a4 = 87
a1 + a2 + a3 + a4 = 87 - 34 = 53

Now we have the sums of the first 4 and last 4 observations. We can calculate the median by finding the middle value in the ordered set of observations:

a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 = 26 + 53 + 34 = 113

Since there are 9 observations, the median will be the 5th value in the ordered set. We can calculate the median as follows:

a1 + a2 + a3 + a4 + a5 = 26
a1 + a2 + a3 + a4 = 53
a1 + a2 + a3 = 53 - a4
a1 + a2 = 53 - a3
a1 = 53 - a2

Substitute the values of a1, a2, a3, and a4 into the total sum equation:
53 - a2 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 = 113
53 + a3 + a4 + a5 + a6 + a7 + a8 + a9 = 113
53 + 61 = 113
113 = 113

Therefore, the median of the set is 53.

The sum of first 5 observation=26
=> Sum of last 4 observation=34-26=8
=> Sum of all 9 observation=26+8=34
=> Mean of 9 observation=34/9=3.77...
=> Median of the 9 observation is 4