Sometimes it will be the case in the exam that you are given the mean or the range and asked to work backwards to find out a particular value. We are going to look at answering questions like this in this section and the next section. The best way to understand how to answer these types of questions is to have a look at a few examples. We are going to be looking at questions that involve the range in this section and questions that involve the mean in the next section.
Example 1 – Range
I am measuring the weight of individuals in a rugby team. The range of weights for the individuals is 5 kg. One individual has a weight of 87 kg.
A) What is the potential maximum weight of an individual in the rugby team?
B) What is the potential minimum weight of an individual in the rugby team?
Part A
Part A asks us to find the potential maximum weight of an individual in the rugby team. We are only able to find the potential maximum weight and not the actual maximum weight because we do not know where the individual that weighs 87 kg lies in the data set; we do not know if he is the largest, smallest or somewhere in between.
We are told in the question that the range of weights in the rugby team is 5 kg. We also know that the range is worked out by taking the smallest value away from the largest value.
We are looking for the potential maximum weight of the individuals. In order to find this, we assume that the individual that has a weight of 87 kg is the lightest individual in the team. Therefore, we add the range onto the assumed smallest weight (87 kg).
I am measuring the weight of individuals in a rugby team. The range of weights for the individuals is 5 kg. One individual has a weight of 87 kg.
A) What is the potential maximum weight of an individual in the rugby team?
B) What is the potential minimum weight of an individual in the rugby team?
Part A
Part A asks us to find the potential maximum weight of an individual in the rugby team. We are only able to find the potential maximum weight and not the actual maximum weight because we do not know where the individual that weighs 87 kg lies in the data set; we do not know if he is the largest, smallest or somewhere in between.
We are told in the question that the range of weights in the rugby team is 5 kg. We also know that the range is worked out by taking the smallest value away from the largest value.
We are looking for the potential maximum weight of the individuals. In order to find this, we assume that the individual that has a weight of 87 kg is the lightest individual in the team. Therefore, we add the range onto the assumed smallest weight (87 kg).
Therefore, the potential maximum weight of the rugby players is 92 kg.
Part B
Part B asks us to find the potential minimum weight of an individual in the rugby team. We find the potential minimum weight by assuming that the individual that weighs 87 kg is the heaviest in the team (largest value). The range is still 5 kg, so we find the potential minimum weight of an individual in the team by taking the range (5 kg) off of the assumed largest value (87 kg).
Part B
Part B asks us to find the potential minimum weight of an individual in the rugby team. We find the potential minimum weight by assuming that the individual that weighs 87 kg is the heaviest in the team (largest value). The range is still 5 kg, so we find the potential minimum weight of an individual in the team by taking the range (5 kg) off of the assumed largest value (87 kg).
Therefore, the potential minimum weight of an individual in the team 82 kg.
The Rule – Range
Here are the rules when we are given a value in the data, the range of the data and asked to find out the potential maximum and minimum.
If we are finding the potential maximum value, we assume that the value that we are given is the smallest value in the data set. We then add the range on to the value that we are given.
Here are the rules when we are given a value in the data, the range of the data and asked to find out the potential maximum and minimum.
If we are finding the potential maximum value, we assume that the value that we are given is the smallest value in the data set. We then add the range on to the value that we are given.
If we are finding the potential minimum value, we assume that the value that we are given is the largest value. We then take the range off the value that we are given.