Question

the median age of the science teachers at mikes school is the same as the median age of the math teachers, but the ages of the math teachers show greater variability. which statement most likely describes the data sets? the difference in ages between the oldest and youngest math teachers is greater than the difference in ages between the oldest and youngest science teachers. there are more math teachers than science teachers at mikes school. the oldest teacher in mikes school is a mathematics teacher. the average age of the math teachers at mikes school is greater than the average age of the science teachers.

Explanation:

Step1: Understand variability

Variability in data can be measured by range (difference between maximum and minimum values). Greater variability implies a larger range.

Step2: Analyze each option

• First option: Since math teachers' ages have greater variability, the range (difference between oldest and youngest) for math teachers is larger than for science teachers. This aligns with the concept of variability.
• Second option: Number of teachers (count) has no relation to variability (spread of data).
• Third option: Just because math teachers' age data has greater variability doesn't mean the oldest teacher is in the math group. Variability is about spread, not individual extreme values in comparison.
• Fourth option: Variability (e.g., range) and average (mean) are different measures. Greater variability of math teachers' ages doesn't imply a greater average age.

Answer:

The difference in ages between the oldest and youngest math teachers is greater than the difference in ages between the oldest and youngest science teachers.