Question

janelle made ordered lists of the heights, in inches, of the students in ms. carvers and mr. wrights homerooms. she found the two lists had the same median value, but the list from ms. carvers class showed greater variability. if the shortest student in mr. wrights homeroom is 48 inches tall and the tallest student is 64 inches tall, what could be the heights of the shortest and tallest students in ms. carvers homeroom?
46 inches and 61 inches
47 inches and 66 inches
52 inches and 63 inches
53 inches and 68 inches

Explanation:

Step1: Recall the concept of variability

Variability is related to the spread of data. A greater - variability means a larger range (difference between the maximum and minimum values). The range of heights in Mr. Wright's homeroom is $64 - 48=16$ inches.

Step2: Calculate the ranges of each option

For option A: Range = $61 - 46 = 15$ inches.
For option B: Range = $66 - 47 = 19$ inches.
For option C: Range = $63 - 52 = 11$ inches.
For option D: Range = $68 - 53 = 15$ inches.

Step3: Select the option with a larger range

Since the list from Ms. Carver's class has greater variability (larger range) than Mr. Wright's class (range = 16 inches), the option with a range greater than 16 inches is option B.

Answer:

B. 47 inches and 66 inches