Question

Given below are the box and whisker plots of the random samples of the weights of $50$ people in two localities, locality $1$ and locality $2$. Which of the following statements is true?

• A. The measure of the center for data $1$ is less than that of data $2$, and the variation for data $1$ is less than that of data $2$.
• B. The measure of the center for data $1$ is less than that of data $2$, and the variation for data $1$ is greater than that of data $2$.
• C. The measure of the center for data $1$ is greater than that of data $2$, and the variation for data $1$ is less than that of data $2$.
• D. The measure of the center for data $1$ is greater than that of data $2$, and the variation for data $1$ is greater than that of data $2$.

Answer 1

The correct option is A The measure of the center for data $1$ is less than that of data $2$, and the variation for data $1$ is less than that of data $2$.

Data 1:
Measure of center, median $=42$
IQR $=$ Third quartile $-$ First quartile $=50-40=10$

Data 2:
Measure of center, median $=50$
IQR $=$ Third quartile $-$ First quartile $=65-45=20$
So, we can say that the measure of the center for data $1$ is less than that of data $2$, and the variation for data $1$ is less than that of data $2$.