Question

The following are historical data on staff salaries (dollars per pupil) for 30 schools sampled in the eastern part of the United States in the early 1970s. 3.79 2.99 2.77 2.91 3.10 1.84 2.52 3.22. Use the data to construct a box plot.

Answer 1

To construct a box plot from the given data, organize the values in ascending order, calculate the median, lower quartile, upper quartile, and draw the plot accordingly.

Step-by-step explanation:

To construct a box plot using the provided staff salaries (dollars per pupil) data (3.79, 2.99, 2.77, 2.91, 3.10, 1.84, 2.52, 3.22), follow these steps:

Organize the data in ascending order: 1.84, 2.52, 2.77, 2.91, 2.99, 3.10, 3.22, 3.79.

Find the median (the middle value) of the dataset. With an even number of data points, the median will be the average of the middle two numbers: (2.91 + 2.99) / 2 = 2.95.

Determine the lower quartile (Q1), which is the median of the first half of the data: (2.52 + 2.77) / 2 = 2.645.

Determine the upper quartile (Q3), which is the median of the second half of data: (3.10 + 3.22) / 2 = 3.16.

Identify any outliers, but in this dataset, there are none apparent.

Draw a box plot with a box from Q1 to Q3, a line inside the box at the median, and 'whiskers' that extend from the minimum to Q1 and from Q3 to the maximum value in the dataset.

Make sure to scale your plot according to the values in the dataset for accurate representation.