David enjoys spending some of his spare time on the golf course.
This week David has played 4 games of golf.
For these games his modal score was 76 and his mean score was 75.
David’s range of scores was 10.
What were his scores for the 4 games?
Answer:
Modal of 76 means that at least two of the scores were 76, however if three were 76 then the mean would be less than 75:
ie (3 x 76 + 66)/4 = 73.5 (NB as the range is 10, the remaining score would have to be 66)
So, we know that one of the two remaining scores is more than 76 (to bring the mean average up to 75) and one must be less than 76 (otherwise the mean would be >75)
We also know that the sum of the remaining two numbers is:
75 x 4 – (76 x 2) = 148
These two numbers have a range of 10 so:
x + (x +10) = 148
2x = 138
x = 69
So the scores are:
69, 76, 76, 79