Examine the three samples listed here. Without performing any calculations, indicate which sample has the largest amount of variation and which sample has the smallest of variation. Explain how you produced your answer.
a) 17 29 12 16 11
b) 22 18 23 20 17
c) 24 37 6 39 29
Which has the largest spread between high and low score?
To determine which sample has the largest amount of variation and which one has the smallest, we can look at the range of each sample. The range measures the difference between the highest and lowest values in a dataset.
Let's analyze each sample:
a) 17 29 12 16 11
The highest value is 29, and the lowest value is 11. Therefore, the range is 29 - 11 = 18.
b) 22 18 23 20 17
The highest value is 23, and the lowest value is 17. Therefore, the range is 23 - 17 = 6.
c) 24 37 6 39 29
The highest value is 39, and the lowest value is 6. Therefore, the range is 39 - 6 = 33.
Based on the range, we can conclude that sample c) (24 37 6 39 29) has the largest amount of variation since it has the highest range of 33. On the other hand, sample b) (22 18 23 20 17) has the smallest amount of variation, as it has the lowest range of 6.