Question

the histogram represents the distribution of lengths, in inches, of 25 catfish caught in a lake. if possible, find the mean. if not possible, explain why not.

Explanation:

Step1: Determine the mid - points of each class

Assume the class intervals are 3 - 6, 6 - 9, 9 - 12, 12 - 15, 15 - 18. The mid - points $x_i$ are $\frac{3 + 6}{2}=4.5$, $\frac{6+9}{2}=7.5$, $\frac{9 + 12}{2}=10.5$, $\frac{12+15}{2}=13.5$, $\frac{15 + 18}{2}=16.5$ respectively.

Step2: Determine the frequencies $f_i$

From the histogram, the frequencies are $f_1 = 4$, $f_2=9$, $f_3 = 5$, $f_4=6$, $f_5 = 1$.

Step3: Calculate the product $f_ix_i$ for each class

$f_1x_1=4\times4.5 = 18$, $f_2x_2=9\times7.5 = 67.5$, $f_3x_3=5\times10.5 = 52.5$, $f_4x_4=6\times13.5 = 81$, $f_5x_5=1\times16.5 = 16.5$.

Step4: Calculate the sum of $f_ix_i$ and $\sum f_i$

$\sum f_ix_i=18 + 67.5+52.5 + 81+16.5=235.5$, $\sum f_i=4 + 9+5+6+1=25$.

Step5: Calculate the mean $\bar{x}$

The mean $\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{235.5}{25}=9.42$.

Answer:

$9.42$