Summer Camp Statistics: Age and Inspiration
What does the median age of 12 for the campers imply?
A. At least one camper is 12 years old
B. If there is an 11-year-old camper, there is also a 13-year-old
C. The mode of the campers’ ages is 12
Final answer:
The median age of the 9 campers is 12, meaning that when the ages are arranged in ascending order, the fifth record is 12. This implies one camper being aged 12. The presence of an 11-year-old camper does not guarantee a 13-year-old one unless specific positions are filled by these ages. Moreover, 12 being the mode isn't definitive as it depicts the most frequently occurring age, which could be any.
Explanation:
In the field of Statistics, the term median refers to the middle value of a set of values. Because it's mentioned that there are 9 campers and their median age is 12, it implies that when all the ages are arranged in ascending order, the fifth one is 12.
A. It is indeed true that at least one of the campers is 12, specifically, the one positioned in the middle of the ordered list of ages.
B. The statement that 'If there is an 11-year-old camper, there is also a 13-year-old' could be true but isn't necessarily the case. It would only be true if the 11-year-old is ranked fourth and the 13-year-old sixth when the ages are arranged in ascending order.
C. The statement 'The mode of campers' ages is 12' might not necessarily be true as mode corresponds to the most frequently occurring value in a set. In this scenario, it could be any age, based on the ages distribution of the campers.