Question

A box-and-whisker plot titled move length in minutes is shown. the number line goes from 80 to 400 in increments of 10. the whiskers range from 81 to 138, and the box ranges from 95 to 128. a line divides the box at 108. what percent of the data lies between 109 minutes and 138 minutes? 25% 50% 75% 100%

Answer 1

In a box-and-whisker plot, the box represents the middle 50% of the data, split evenly around the median. The data between 109 minutes and 138 minutes falls in the upper quartile, representing 25% of the data.

Step-by-step explanation:

The question revolves around a box-and-whisker plot that displays movie lengths. According to the information given, the box ranges from the first quartile at 95 minutes to the third quartile at 128 minutes, and the median is located at 108 minutes. We know that the box represents the middle 50% of the data. Therefore, the data falling between the median (109 minutes, not inclusive of 108 minutes median line) and the third quartile (138 minutes) represents 25% of the data. This is because the total spread of the box, which represents 50% of the data, is divided into two equal parts by the median. One part represents the data between the first quartile and median (95 to 108 minutes), and the other part represents the data between the median and third quartile (108 to 128 minutes). The whisker then extends from the third quartile to the maximum value which is 138 minutes, thus the range 109 to 138 minutes is within the upper quartile, representing 25% of the data.

Answer 2

In a box-and-whisker plot with the given data, more than 25% but less than 50% of the data lies between 109 and 138 minutes. The exact percentage cannot be determined from the information provided, but it is more than the 25% accounted for by the data within the box from 109 to 128 minutes.

Step-by-step explanation:

The student's question is related to understanding the percentage of data within a given range on a box-and-whisker plot. In this specific plot, the box ranges from 95 to 128 minutes and is divided by a line at 108 minutes, which represents the median. The right whisker extends from 128 to 138 minutes.

Since the question asks for the percentage of data between 109 to 138 minutes, we are looking at data above the median up to the maximum (138). The box represents the middle 50% of the data, so the data from 109 to 128 minutes would be half of that, accounting for 25%. Additionally, the data from 128 to 138 minutes is part of the upper whisker, lying outside the box. The whiskers represent the lowest and highest 25% of the data, but since we are only considering the part from 128 to 138 minutes, it is less than 25%. Thus, combining the two portions, it is more than 25% but less than 50% of the data that lies between 109 and 138 minutes. Without the exact distribution of the data in the whisker, we cannot determine the precise percentage, but we know that it must be greater than 25% and less than 50%.

However, the student's question provided options of 25%, 50%, 75%, or 100%. Given our analysis, none of these options are correct if we are to provide a precise answer. Still, the closest approximate answer from the options given would be 25%, which only takes into account the data within the box from 109 to 128 minutes, but this is not entirely accurate since it neglects the data in the whisker from 128 to 138 minutes.