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Video: Verifying the Range of a given Data Set

Tim Burnham

The number of goals scored by twelve soccer players in a season are 13, 11, 12, 5, 5, 9, 6, 11, 8, 5, 6, and 19. State whether the following statement is true or false: The range of the data is 14 goals.


Video Transcript

The numbers of goals scored by twelve soccer players in a season are thirteen, eleven, twelve, five, five, nine, six, eleven, eight, five, six, and nineteen. Find the range of the numbers of goals scored.

Well before we answer this question, let’s have a little think about what the data actually means. And to do that, we’re just gonna create a little table. First of all, we’ve got a row that tells us the number of goals and then we’ve got the number of players scoring that many goals.

So among those twelve players, three of them scored five goals each; two of them scored six goals each; nobody scored exactly seven goals; but one player scored eight goals; one player scored nine goals; nobody scored exactly ten goals; but two players scored eleven goals one player scored twelve goals; and one scored thirteen goals; and this super striker scored nineteen goals.

So for this particular group of twelve players, the smallest number of goals that any of them scored in the entire season was five. In other words, everyone scored at least five goals. And the largest number of goals that anybody scored was nineteen. So everybody scored between five and nineteen goals, so that’s the range of our data.

The minimum number of goals scored was five, and the maximum number of goals scored was nineteen. So the range is the difference between these two. And to work out the difference between the minimum and the maximum number of goals scored, we just calculate the maximum take away the minimum. So that’s gonna be nineteen take away five, which is fourteen.

So the answer is that the range is fourteen goals. And this means that the difference in the number of goals scored between the highest scoring player, the most prolific goal scorer, and the person who scored the least number of goals is a difference of fourteen goals.