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Give an example of a data set where this statement is false: "minimum < mean < maximum" - Junior Cycle Mathematics - Question 8 - 2015
Question 8
Give an example of a data set where this statement is false: "minimum < mean < maximum". Describe for what kind of data sets this statement is false: "minimum < m... show full transcript
Worked Solution & Example Answer:Give an example of a data set where this statement is false: "minimum < mean < maximum" - Junior Cycle Mathematics - Question 8 - 2015
Step 1
Give an example of a data set where this statement is false:
Answer
Consider the data set containing a single number, for example, {1}. In this case, the minimum, mean, and maximum are all equal:
- Minimum = 1
- Mean = 1
- Maximum = 1
Thus, we have:
This clearly shows that the statement "minimum < mean < maximum" is false.
Step 2
Describe for what kind of data sets this statement is false:
Answer
For the statement "minimum < mean < maximum" to be false, we need situations where the mean is equal to either the minimum, maximum, or both. This occurs in two scenarios:
- Single Element Data Set: If the data set contains only a single element, the minimum, mean, and maximum are identical. For example, {5}.
- Identical Elements: If all elements in the data set have the same numerical value, then the minimum, mean, and maximum will be the same. For example, {2, 2, 2}.
In both cases, the standard deviation is zero, indicating no variation in the data.