e are being asked to answer the following questions: 1. How many students got 5 ? 2. How many students got below 3 ? 3. If the passing score is 4 , how many passed the quiz? 4. What was the lowest score obtained by a student?

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1. To determine how many students got a score of $$5$$, we need the frequency (or count) assigned to that score. In other words, if we let $$f(5)$$ be the number of students scoring $$5$$, then the answer is  
$$
f(5).
$$

2. To find how many students scored below $$3$$, we typically sum the frequencies for the scores that are less than $$3$$. For example, if the scores are $$0, 1, 2, \ldots, 5$$ with frequencies $$f(0)$$, $$f(1)$$, $$f(2)$$, $$\dots$$ respectively, then the total number of students scoring below $$3$$ is  
$$
f(0) + f(1) + f(2).
$$

3. If the passing score is $$4$$, then any score of $$4$$ or $$5$$ is considered passing. Thus, the number of students who passed the quiz is given by  
$$
f(4) + f(5).
$$

4. The lowest score obtained by a student is found by identifying the smallest score for which the corresponding frequency is positive. If we denote the scores in increasing order (for example, $$0, 1, 2, 3, 4, 5$$) and if there exists a score $$s_{\text{min}}$$ such that  
$$
f(s_{\text{min}}) > 0,
$$
and for all $$s < s_{\text{min}}$$ we have  
$$
f(s) = 0,
$$
then $$s_{\text{min}}$$ is the lowest score obtained.

*Note:* To obtain numerical answers, the actual frequency distribution (i.e. the values for $$f(0), f(1), \ldots, f(5)$$) must be provided. Without those specific data, we can only express the answers in this general form.
1. The number of students who got a score of 5 is $$ f(5) $$. 2. The number of students who scored below 3 is $$ f(0) + f(1) + f(2) $$. 3. The number of students who passed the quiz (with a passing score of 4) is $$ f(4) + f(5) $$. 4. The lowest score obtained by a student is the smallest score $$ s_{\text{min}} $$ where $$ f(s_{\text{min}}) > 0 $$.

e are being asked to answer the following questions: 1. How many students got 5 ? 2. How many students got below 3 ? 3. If the passing score is 4 , how many passed the quiz? 4. What was the lowest score obtained by a student?

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