Question

Researchers studying catfish estimated the number of fingerling catfish and large catfish living in different rivers throughout the country. The above histograms summarize the relative frequency for each type of catfish.

Based on the histograms, which of the following is the best comparison of the means and the ranges for the two distributions?
A) The mean and range of the fingerling catfish are both equal to those of the large catfish.
B) The mean and range of the fingerling catfish are both less than those of the large catfish.
C) The mean and range of the fingerling catfish are both greater than those of the large catfish.
D) The mean of the fingerling catfish is equal to that of the large catfish, and the range of the fingerling catfish is greater than that of the large catfish.
E) The mean of the fingerling catfish is equal to that of the large catfish, and the range of the fingerling catfish is less than that of the large catfish.

Answer 1

The correct answer to the question is

C) The mean and range of the fingerling catfish are both greater than those of the large catfish.

Explanation:

From the attached chart and table, it is seen that the mean = (∑ f×m)/n

Where Mean x = Mean estimate of frequency distribution

f = Class frequency

m = midpoint of each class

∑ f×m = the sum of the product of each midpoint value and its respective frequency

n = The sum of the frequencies

Therefore from the tables we have

For the Fingerling catfish

(∑ f×m)/n = 11037.5/1.375 = 8027.3

and the range = (Maximum value) - (minimum value) in the data set

= 10500 - 3500 = 7000

For the Large catfish we have

(∑ f×m)/n = 2931.25/2.1 = 1395.83

and the range = (Maximum value) - (minimum value) in the data set

= 2125 - 375 = 1750

As seen above, the mean and range of the fingerling catfish are both greater than those of the large catfish