Question 17

Explanation

We will combine all apple mass data from Ferdian and Belle, sort it, and then evaluate each statement.

Combining and Sorting Data

Ferdian's apple mass data (with $x = 180$):

Belle's apple mass data:

Combined data (total $12$ apples):

Sorted data from smallest to largest:

Total data ($n$) = $12$.

Evaluating First Statement

Statement: $25\%$ of the smallest apples have a mass of $< 162 \text{ grams}$.

We calculate $25\%$ of the total data:

The $3$ smallest data points are $154$, $157$, $161$. All these values are less than $162$ grams.

Conclusion: First statement is TRUE.

Evaluating Second Statement

Statement: $25\%$ of the largest apples have a mass of $> 180 \text{ grams}$.

We calculate $25\%$ of the total data:

The $3$ largest data points are $182$, $180$, $180$. Not all of these are greater than $180$ (since two values are exactly $180$).

Conclusion: Second statement is FALSE.

Evaluating Third Statement

Statement: $50\%$ of the smallest apples have a mass of $< 170 \text{ grams}$.

We calculate $50\%$ of the total data:

The $6$ smallest data points are $154$, $157$, $161$, $162$, $163$, $167$. The largest value in this group is $167$, which is less than $170$.

Conclusion: Third statement is TRUE.

So, the sequence of truth is TRUE - FALSE - TRUE.