The data below shows the masses of 40 boxes at the port in kilograms.

128, 100, 116, 146, 102, 84, 116, 92, 116, 120,
90, 96, 138, 96, 100, 86, 104, 128, 116, 92,
118, 108, 82, 122, 146, 98, 148, 110, 88, 146,
106, 134, 124, 94, 132, 104, 120, 122, 108, 140.

(a) Starting with the class 80 – 89, draw a frequency table.
(b) Calculate the median mass.

To solve this problem, we need to complete two tasks: create a frequency table with specified class intervals and calculate the median mass of the given data.

(a) Frequency Table:
First, we'll create a frequency table starting with the class interval 80 – 89. We will set up the classes to be continuous, with a width of 10 for each class interval:

Mass (kg)Frequency80 - 89590 - 998100 - 1097110 - 1197120 - 1296130 - 1393140 - 1494

Creating the table:

80 - 89: Count the numbers 84, 86, 82, 88, which gives us a frequency of 4.
90 - 99: Count the numbers 90, 92, 92, 96, 96, 98, which gives us a frequency of 6.
100 - 109: Count the numbers 100, 100, 102, 104, 106, 104, 108, 108, which gives us a frequency of 8.
110 - 119: Count the numbers 116, 116, 116, 118, 116, 116, which gives us a frequency of 6.
120 - 129: Count the numbers 120, 120, 122, 122, 124, 128, 128, which gives us a frequency of 7.
130 - 139: Count the numbers 132, 134, 138, which gives us a frequency of 3.
140 - 149: Count the numbers 140, 146, 146, 146, 148, which gives us a frequency of 5.

(b) Calculating the Median Mass:
To find the median, first, we need to arrange the data in ascending order. The ordered data is:

82, 84, 86, 88, 90, 92, 92, 94, 96, 96, 98, 100, 100, 102, 104, 104, 106, 108, 108, 110, 116, 116, 116, 116, 116, 118, 120, 120, 122, 122, 124, 128, 128, 132, 134, 138, 140, 146, 146, 146, 148

There are 40 data points in total. The median is the average of the 20th and 21st values in the ordered list:

20th value: 108
21st value: 116

Median = [tex]\frac{108 + 116}{2} = 112[/tex]

Therefore, the median mass is 112 kg.