Stats math help - i need help with this frequency distribution question?

Question

The frequency distribution below lists the number of hours per day a randomly selected sample of teenagers spent watching television.

hours per day *** number of teenagers

(0-1) .... 10

(1-2)...... 59

(2-3)........27

(3-4)........35

(4-5)....... 34

(5-6)....... 13

(6-7)....... 17

n = 195

What percent of the teenagers watch more than 3.5 hours per day?

help, i dont know how to solve with the 3.5...

thanks

Answer 1

You could draw the histogram, fit a curve to it and cut it at 3.5 hours per day. Count those to the right of the line and express it as a% of 195.

If you cannot do that, your best bet is to assume that those in the 3-4 hour bracket are distributed across the interval in the ratio of the numbers in the intervals to either side. Hence those above 3.5 hours would be 35*34/(34+27) =19.51. Since you cannot have a partial student, call it 20, add to 34+13+17 and express the total as a % of 195.    

84/195 = 43%

This estimate is probably as good as you can get out of the data

Answer 2

It would be helpful to know what the asker of this question was trying to test.  Since we don't know that, we can only give you guesses as to what the asker was looking for in an answer.

So here a couple more guesses.

You seem be able to determine if an answer is correct.  

So if 41.5384...% is the answer, that was achieved by assuming a normal distribution of the (3-4) range and assining a value of 3.5 hours to one teenager with 17 on either side giving 81/195.

Or 41.7948...% would come from assuming 17.5 students on either side of the mid point.