Question

Which statement is true about the data sets Set A and Set B, given that Set A contains the values 5, 5, 5, 5, 5, and Set B contains the values 2, 2, 2, 2, 17?

Answer 1

Comparison of Set A and Set B reveals distinct differences in mean and range, with Set A being uniform and Set B showing more variation. Statements typically related to box plots are not entirely applicable here as these statements reflect different contexts and characteristics than the given Sets A and B.

Step-by-step explanation:

When comparing Set A (5, 5, 5, 5, 5) and Set B (2, 2, 2, 2, 17), it is clear that some statistics such as the mean (average value) and range (difference between the largest and smallest values) will differ between the two sets. Set A has a mean of 5 and a range of 0, as all elements are the same. Set B has a mean of 5 ((2+2+2+2+17)/5) and a range of 15 (17-2), displaying more variation within the dataset.

Focusing specifically on statements related to box plots and data characteristics, we can determine that:

1. For Set A, it's true that 25% of data are at most 5 because all the values are 5. Of course, this also means that 100% of the data are at most 5.
2. There can't be the same amount of data from 4-5 as from 5-7 in Set A because all data are precisely 5.
3. There are indeed no data values of three in either set.
4. Fifty percent of the data being four is not applicable to these sets, as Set A has all values of 5 and Set B does not have the number 4 at all.

When looking at the outcomes for A AND B and A OR B as found in a different context, it is important to understand that A AND B refers to the intersection (common elements) of two sets, while A OR B refers to the union of all elements from both sets. This is a topic surrounding basic set theory.