Need help to find possible smallest and largest value of x

[Durjoy]

The number of goals scored in a series of football matches was as follows:
No. of Goals : 1 2 3
No. of Matches: 8 8 x
a) If the mean number of goals is 2.04, find x -----> 9
b)If the modal value number of goals is 3, find the smallest possible value of x ---------> 9
c) If the median number of goals is 2, find the largest possible value of x.
As you can see I know a and b but not c. Please can you explain how you get the answer? Thanks!

 

[Dr.Peterson]

Presumably you solved (a) by writing an equation that said the mean is 2.04, and (b) by thinking about what it means for the mode to be 3.

Do the same here. How would the median be 2? You might imagine lining up the numbers in order: 1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,... . What does it take for the median (the middle number) to be 2?

 

[Durjoy]

I understand that.. If the median is 2..that means if I devide n/2 than the number will contain in the 2,2,2,2,2,2,2,2

 

[Dr.Peterson]

I understand that.. If the median is 2..that means if I devide n/2 than the number will contain in the 2,2,2,2,2,2,2,2

So, what values can you have for n/2?

 

[Durjoy]

If I count from 1,1,1,1,1,1,1,1
........................ 2,2,2,2,2,2,2,2 here if we go for median 2 and stop counting in the column of 2... 9,10,11,12,13,14,16 which will be for median 2

 

[Dr.Peterson]

I'm not sure what this means. What is your answer?