Question

The average of the values of 19 observations, arranged in ascending order, is 23. If the value of 1st observation is 11 and no two observations have same values, what is the maximum possible value of the 19th observation ?

Answer 1

The following question is a combination of sequence and series and statistics
We know that,
Average of n observations=(x1+x2+x3+x4+...xn)/n
 where x1,x2 are the respective observations
now,
we can also state that x1+x2+x3...xn=Sum of all observations
So,
Substituting values from above question
Average=23
No of observations=19
23=(Sum of observations)/19
Sum of observations =23*19
                                     =437

now,
x1+x2+x3+....xn=437
But in the question it is mentioned that  the observations are arranged in ascending order
and no two observations are saqme
It is given that x1=11
So in order to make x19 greatest x1+x2+x3+...x18 should be the least
so we can achieve this by assuming least common difference between them as d=1
Now it is known that
Sum of terms of a finite AP is
Sn=n/2  * (2a+(n-1)d)
a=11
d=1
n=18
Sn=18/2  *(2*11+(18-1)1)
    =9*39
     =351

We know that from earlier data that sum of observations is 437
So,
x19+351=437
 
x19=437-351
x19=86
So
The maximum possible value of 19th observation is 86

Answer 2

Answer:

Step-by-step explanation:

88