Question

rick wants to know the height of the students in seventh - grade. he randomly notes the heights of 15 students from each seventh - grade class. the mean and median heights of the students are 56 inches and 46 inches, respectively. which statement must be true?

about one - half of the students are more than 56 inches tall

on average, the students are 46 inches tall

on average, the students are 56 inches tall

about one - half of the students are more than 46 inches tall

Explanation:

Step1: Recall mean and median definitions

The mean is the average value of a data - set. The median is the middle value when the data is arranged in ascending or descending order. Half of the data values are greater than the median and half are less than the median.

Step2: Analyze each option

• Option 1: The mean is 56 inches, not the median. We cannot say about half of the students being more than 56 inches based on the given information.
• Option 2: The mean is 56 inches, not 46 inches. So, on average, students are not 46 inches tall.
• Option 3: Since the mean height is 56 inches, on average, the students are 56 inches tall.
• Option 4: Since the median height is 46 inches, about one - half of the students are more than 46 inches tall.

Answer:

C. On average, the students are 56 inches tall; D. About one - half of the students are more than 46 inches tall