Question

He stemplot below displays the grades (out of 30) that 26 students received on a quiz. a stemplot titled quiz grades has values 12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30. which of the following boxplots correctly displays the distribution of quiz grades? a boxplot. a number line labeled quiz grades goes from 12 to 30. points are at 12, 14, 15, and 16. the whiskers range from 20 to 30, and the box ranges from 23 to 27. a line divides the box at 25. a boxplot. a number line labeled quiz grades goes from 12 to 30. the whiskers range from 12 to 30, and the box ranges from 23 to 27. a line divides the box at 25. a boxplot. a number line labeled quiz grades goes from 12 to 30. points are at 12 and 14. the whiskers range from 15 to 30, and the box ranges from 22 to 27. a line divides the box at 25. a boxplot. a number line labeled quiz grades goes from 12 to 30. the whiskers range from 12 to 30, and the box ranges from 18 to 27. a line divides the box at 24.

Answer 1

The correct boxplot must be constructed using the five-number summary that includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values determined from the stemplot. No specific boxplot is selected since the actual values for Q1, median, and Q3 are not provided in the data. The answer provides a method to construct and match the correct boxplot to the data.

Step-by-step explanation:

To determine which boxplot correctly displays the distribution of the given quiz grades, we must consider the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values from the stemplot provided. The boxplot will consist of the five-number summary: the smallest value (minimum), Q1, median (the middle value when the data is ordered), Q3, and the largest value (maximum). These values can be determined from the stemplot to accurately construct and match the boxplot.

The minimum and maximum values are given by the smallest and largest grades, respectively. For these grades, 12 is the minimum and 30 is the maximum. The median will split the dataset into two halves, so with 26 students, the median will be the average of the 13th and 14th scores when sorted. The first quartile (Q1) is the median of the lower half, excluding the median of the dataset if it is part of the data, and the third quartile (Q3) is the median of the upper half, also excluding the median of the dataset if it is part of the data. With these quartiles, we can construct our boxplot. The whiskers extend from the ends of the box (Q1 and Q3) to the minimum and maximum values, unless there are outliers, which would be marked as separate points.