Question

use the box - and - whisker plot to answer the questions below.
(a) which of these best describes the lengths (in centimeters) of the fish caught during the competition?
there were more fish with a length under 50 than with a length over 50.
there were more fish with a length over 50 than with a length under 50.
the same number of fish had a length under 50 as had a length over 50.
(b) which of the following intervals gives the middle 50% of the data?
50 to 54
50 to 53
53 to 54
43 to 53
(c) what is the difference of the longest length and the shortest length of fish caught during the competition? (that is, what is the range of the data?)

Explanation:

Part (a)

In a box - and - whisker plot, the median (the line inside the box) divides the data into two halves. If we look at the plot, the median is around 50 - 53 (from the box). The number of data points below the median (length under 50) and above the median (length over 50) should be the same because the median splits the data set into two equal - sized groups. So the statement "The same number of fish had a length under 50 as had a length over 50" best describes the lengths of the fish.

The middle 50% of the data in a box - and - whisker plot is represented by the inter - quartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). The box in the box - and - whisker plot represents the middle 50% of the data. From the plot, the interval that corresponds to the box (middle 50% of the data) is 50 to 53.

Step 1: Identify the shortest and longest lengths

From the box - and - whisker plot, the shortest length (minimum value) is 43 (from the left whisker) and the longest length (maximum value) is 70 (from the right whisker).

Step 2: Calculate the difference

To find the difference between the longest and shortest lengths, we use the formula \( \text{Difference}=\text{Longest length}-\text{Shortest length} \). Substituting the values, we get \( 70 - 43=27 \).

Answer:

The same number of fish had a length under 50 as had a length over 50.

Part (b)