Question

Which element of variation would not be affected by adding the data value 15 to the data set {3, 5, 6, 8, 9, 10, 13, 14}?

Answer 1

please help

Answer 2

The elements of variation are Mean, Median, Mode, and Range. So, we'd like to compare these 4 elements from the original set to what they would look like with 15 added to the set.

The Mean we find by adding all the numbers in the set and dividing by the total number of numbers. The original Mean is 8.5 and the number we're adding is larger than that, so the Mean will increase.

The Median is found by seeing which number is in the middle of the list of numbers. Again, this value is 8.5 (there's no one middle number, so average the two middle numbers 8 and 9). Again, we're adding a number larger than that to the set, so the Median will increase.

The Range is found by taking the difference between the largest number and smallest number. Originally, this value is 14 - 3 = 11. When we add 15 to the set, that becomes the largest number, so now the Range is 15 - 3 = 12.

Finally, the Mode is found by seeing which number occurs most often in the set. Originally, there is no Mode since each number just appears once. That doesn't change when we add a 15 to the set, since that isn't a repeat either. This means the Mode is the element of variation that doesn't change.