Question

A boxplot helps to visualize the variability of a distribution. Five statistics form a boxplot, often referred to as the five-number summary for the distribution. How much of the data is between the first and third quartiles?

1) 25%
2) 50%
3) 75%
4) Cannot be determined

Answer 1

A boxplot shows the middle 50% of the data between the first and third quartiles. Therefore, the data between these quartiles accounts for 50% of the distribution.

Step-by-step explanation:

A boxplot, which provides a visual summary of data, includes five key statistics: the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value. The data between the first and third quartiles represent the interquartile range (IQR), which covers the middle 50 percent of the data.

The percentage of data between the first and third quartiles, by definition, is 50%. This is because quartiles divide the data into four equal parts. Therefore, the area of the box plot between Q1 and Q3 represents the second and third quartiles of the data set, which together account for 50% of the data points. This is a useful measure for understanding the spread and dispersion of the middle portion of the data set.

In conclusion, the correct choice from the given options is 2) 50%