Question

1. the histogram represents the distribution of lengths, in inches, of 25 catfish caught in a lake. (lesson 1 - 2)

a. if possible, find the mean. if not possible, explain why not.
b. if possible, find the median. if not possible, explain why not.
c. were any of the fish caught 12 inches long?
d. were any of the fish caught 19 inches long?

Explanation:

Step1: Recall mean - requirement

To find the mean, we need exact data values or mid - points of intervals and their frequencies. The histogram only shows intervals and frequencies, without mid - points given, so we can't calculate the mean.

Step2: Recall median - requirement

To find the median, we need to know the exact data values or at least be able to order them precisely. Since the histogram gives only intervals, we can't find the median.

Step3: Check for 12 - inch fish

The bar for the 12 - inch length (assuming the intervals are inclusive - exclusive and 12 is in the 12 - 15 interval) has a non - zero height, so there are fish 12 inches long.

Step4: Check for 19 - inch fish

The histogram only goes up to 18 inches, so no fish were 19 inches long.

Answer:

a. Not possible. Need mid - points of intervals and frequencies to calculate mean.
b. Not possible. Need exact data values to order for median.
c. Yes
d. No