Chapter 12.3, Problem 27PPE

To determine

To find: What will be the mean, median, mode, and range of the crocodile’s length after 4 yr.

Answer to Problem 27PPE

After four years.

  $\begin{array}{l}\text{Mean}=2.825\\ \text{Median}=2.8\\ \text{Mode}=2.8\text{ and 2}\text{.9}\\ \text{Range}=0.7\end{array}$

Explanation of Solution

Given information:

  $12$ crocodiles were rescued and their lengths were tagged as below data set. Crocodiles grows $0.1$ m each year.

  

Calculation:

Given data set is −

  

  $\begin{array}{l}\text{Arranging in ascending order: 2}\text{.1 2}\text{.2 2}\text{.3 2}\text{.3 2}\text{.4 2}\text{.4 2}\text{.4 2}\text{.5 2}\text{.5 2}\text{.5 2}\text{.7 2}\text{.8}\\ \text{Here, mean}=\frac{2.4+2.8+2.1+2.5+2.4+2.2+2.5+2.3+2.5+2.3+2.4+2.7}{12}=2.425\\ \text{Median}=\frac{2.4+2.4}{2}=2.4\\ \text{Mode}=2.4\text{ and }2.5\\ \text{Range}=2.8-2.1=0.7\end{array}$

Each crocodiles grows $0.1$ m per year. So, after $4$ years each would have grown by $0.4$ m.

When same amount is added to each value in a data set the mean, median, and mode also shift right by same amount. But the range remains same.

Therefore after four years,

  $\begin{array}{l}\text{Mean}=2.425+0.4=2.825\\ \text{Median}=2.4+0.4=2.8\\ \text{Mode}=2.8\text{ and 2}\text{.9}\\ \text{Range}=0.7\end{array}$