Video: Describing the Effect of an Additional Data Value on the Range of a Data Set

The following figure demonstrates the number of glasses of water a group of people consume per day. Describe how the range would change if an additional data value of 1 was added to the data set.

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Video Transcript

The following figure demonstrates the number of glasses of water a group of people consume per day. Describe how the range would change if an additional data value of one was added to the data set.

The graph tells us that eight people consume zero glasses of water per day. Five people consume one glass; two people consume two glasses; six people, three glasses; one person, four glasses; and, finally, seven people consume five glasses of water per day.

We know that, in order to calculate the range of a data set, we subtract the smallest value from the largest value. In this question, it will be the number of glasses. It doesn’t matter how many different people consume that number of glasses. The smallest value is therefore zero. As there’re some people, in this case, eight, that consume no glasses of water. The largest value is equal to five as this is the greatest number of glasses of water that anybody consumes. We can therefore calculate the range of the original data by subtracting zero from five. This is equal to five.

We are then told that there is an additional data value of one that is added to the data set. This means that there are now six people that consumed one glass of water per day. This does not impact the smallest or largest value though. So the new range is still equal to five minus zero. Adding the extra data value does not alter the range. We can therefore conclude that the range would remain unchanged at five.

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