Answer:
(A) Maximum = 100 kg.
(B) Lower quartile = 55 kg.
(C) Minimum = 45 kg.
(D) Upper quartile = 93 kg.
(E) Median = 81 kg.
Step-by-step explanation:
A box-plot, also known as a box and whisker plot is a method to demonstrate the distribution of a data-set based on the following 5 number summary,
- Minimum (shown at the bottom of the chart)
- First Quartile (shown by the bottom line of the box)
- Median (or the second quartile) (shown as a line in the center of the box)
- Third Quartile (shown by the top line of the box)
- Maximum (shown at the top of the chart).
The data provided for the weight, in kilograms, of 15 containers shipped from a factory in one week is as follows:
S = {45, 51, 53, 55, 55, 65, 75, 81, 84, 87, 93, 93, 95, 96, 100}
The data is already arranged in ascending order.
The maximum value is:
Maximum = 100 kg.
The first quartile is the median value of the first half of the data.
The first half of the data is:
S₁ = {45, 51, 53, 55, 55, 65, 75}
The median of this data set is the middle value, i.e. 4th value.
So, the first quartile is:
Lower quartile = 55 kg.
The minimum value is:
Minimum = 45 kg.
The third quartile is the median value of the second half of the data.
The second half of the data is:
S₂ = {84, 87, 93, 93, 95, 96, 100}
The median of this data set is the middle value, i.e. 4th value.
So, the third quartile is:
Upper quartile = 93 kg.
The The median of the data set is the middle value, i.e. the 8th value.
Median = 81 kg.
