Question

a fishing tournament was held last year at the fishing academy. the organizer recorded the weight of each of the 32 fish caught. the smallest weight was 15 lb, and the largest was 21 lb. the table gives the mean, median, range, and interquartile range (iqr) of the data set. summary values: mean 19, median 20, range 6, iqr 4. (a) select the best description of spread for the data set. we can tell by the mean that the middle half of the data set is 19 units wide. we can tell by the iqr that the middle half of the data set is 4 units wide. we can tell by the number of fish caught that the middle half of the data set is 32 units wide. (b) select the best description of center for the data set. the \average\ fish (in lb) was about 4 to 6, based on the iqr and range. the \average\ fish (in lb) was about 32, which is the number of fish caught. the \average\ fish (in lb) was about 19 or 20, based on the mean and median. (c) select the graph with the shape that best fits the summary values. graph 1 (the data set is not symmetric.) graph 2 (the data set is symmetric.)

Explanation:

Step1: Recall measures of spread and center

The inter - quartile range (IQR) measures the spread of the middle 50% of the data. The mean and median are measures of the center of the data. The range measures the spread between the maximum and minimum values.

Step2: Analyze part (a)

The IQR tells us about the spread of the middle half of the data. So, the statement "We can tell by the IQR that the middle half of the data set is 4 units wide" is correct as the IQR value given is 4.

Step3: Analyze part (b)

The mean and median are measures of the center of the data. Given the mean is 19 and median is 20, the statement "The 'average' fish (in lb) was about 19 or 20, based on the mean and median" is correct.

Step4: Analyze part (c)

Looking at the two graphs, Graph 2 is symmetric as the bars on either side of the center are approximately mirror - images. So, the correct graph for the data set being symmetric is Graph 2.

Answer:

(a) We can tell by the IQR that the middle half of the data set is 4 units wide.
(b) The "average" fish (in lb) was about 19 or 20, based on the mean and median.
(c) Graph 2 (The data set is symmetric.)