Question

These graphs represent the average heights of boys ages 14 to 15 years old and 16 to 17 years old.Based on the data, which statement is true?A. The range is approximately 3 times the difference of the medians.B. The difference of the medians is approximately 1 times the range.C. The range is approximately 12 times the difference of the medians.D. The difference of the medians is approximately 4 times the range.

Answer 1

Suppose that both functions are normal distributions. In a normal distribution, the median is equal to the mean, which corresponds to the line that divides the distribution into two identical parts. Therefore, the difference between the medians is

`68.5-64.5=4`

As for the range, it is defined as the difference between the greatest and the lowest value of the distribution. If we consider the function to consist of two identical distributions whose extreme values are 66-63, and 70-67, the range becomes

`\begin{gathered} 66-63=3 \\ 70-67=3 \\ \Rightarrow\text{range}=3 \end{gathered}`

Therefore, the answer is option B. as the difference of the medians is 4 and the range is 3.