Thread: Help with proof.

Hi! I don't know much about stadistics, so I hope you can help me with this problem.

Consider the following numbers: 2, 3, 3, 4, 1, 2, 2, 1, 0 representing the number of hits garnered by each member of the Baltimore Orioles in a recent outing. (a) Calculate directly the average number of hits per man. (b) Let x be a variable signifying the number of hits obtained by a man, and let f(x) be the number of times the number x appears.

Show that the average number of hits per man can be written as:



The average number of hits per man is 2, am I right? However I don't know how to show part b). Thanks in advance.

Originally Posted by Cesc1

Hi! I don't know much about stadistics, so I hope you can help me with this problem.

Consider the following numbers: 2, 3, 3, 4, 1, 2, 2, 1, 0 representing the number of hits garnered by each member of the Baltimore Orioles in a recent outing. (a) Calculate directly the average number of hits per man. (b) Let x be a variable signifying the number of hits obtained by a man, and let f(x) be the number of times the number x appears.

Show that the average number of hits per man can be written as:



The average number of hits per man is 2, am I right? However I don't know how to show part b). Thanks in advance.

Yes the average number of hits per man is 2 (18 total hits divided by 9 players). For part b) x is a variable which can take on the values of the number of hits obtained by a man. The smallest x can be is 0. So when x is 0, the question is what is f(x), i.e. how many players had 0 hits? Looking at the list the number is clearly 1. Similarly, 2 hitters got 1 hit, so when x=1 then we know f(x)=2.

The average of x is equal to the total number of hits divided by the number of players. To show the quotient of the summations equals this, you should show that the numerator equals the total number of hits and the denominator equals the total number of players.

Thanks dude! Turns out it was really simple.