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.