Question

Which representation would be best for determining between which two values 50% of the data will lie?

0.78, 0.83, 0.85, 0.81, 0.82, 0.83, 0.85, 0.80, 0.80, 0.84, 0.86, 0.79, 0.85, 0.84, 0.82, 0.84, 0.85, 0.82, 0.82, 0.84, 0.83, 0.83, 0.85, 0.84, 0.81, 0.83, 0.81, 0.82, 0.87, 0.86
(A) Boxplot
(B) Histogram
(C) Scatter plot
(D) Frequency polygon

Answer 1

A box plot is the best representation for determining where the middle 50% of the data lies because it clearly shows the median, quartiles, and the interquartile range.

Step-by-step explanation:

To determine between which two values 50% of the data will lie, a box plot (also known as a box-and-whisker plot) would be the most suitable representation. A box plot visually displays the median, quartiles, and the interquartile range (IQR), which represents the middle 50% of a data set. Given the nature of a box plot, you can easily identify the first quartile (Q1) and the third quartile (Q3), and thus the IQR can be observed, showing exactly where the central 50% of the data lies.

In the context provided, a box plot would allow us to see the middle 50% with the box representing the data between the first quartile (25th percentile) and the third quartile (75th percentile), giving us the needed insights.