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Professor Stat gave a 4-question quiz. The results of her class are as follows:

\begin{tabular}{cc}
Score Earned & Number of Students \\
\hline
25 & 14 \\
50 & 23 \\
75 & 19 \\
100 & 8 \\
\end{tabular}

Which of the following statements is true?

A. The data is skewed right.
B. All of the statistics provided are true.
C. The average score earned per student is 58.2.
D. None of the statistics provided are true.
E. The mode is 50.

Sagot :

GinnyAnsweridn
Let's analyze the given data step-by-step to determine which of the statements provided is true.

### Step 1: Calculate the Total Number of Students

First, we need to find the total number of students who took the quiz:

[tex]\[ 14 + 23 + 19 + 8 = 64 \][/tex]

So, there are 64 students in total.

### Step 2: Calculate the Total Score Earned by All Students

Next, we will find the total score earned by all the students:

[tex]\[ (25 \times 14) + (50 \times 23) + (75 \times 19) + (100 \times 8) \][/tex]

Calculating each term:

[tex]\[ 25 \times 14 = 350 \][/tex]
[tex]\[ 50 \times 23 = 1150 \][/tex]
[tex]\[ 75 \times 19 = 1425 \][/tex]
[tex]\[ 100 \times 8 = 800 \][/tex]

Adding these values together:

[tex]\[ 350 + 1150 + 1425 + 800 = 3725 \][/tex]

So, the total score earned by all students is 3725.

### Step 3: Calculate the Average Score

Now, we can calculate the average score per student:

[tex]\[ \text{Average Score} = \frac{\text{Total Score}}{\text{Total Number of Students}} = \frac{3725}{64} \approx 58.203125 \][/tex]

So, the average score is approximately 58.203125.

### Step 4: Determine the Mode

The mode is the score that occurs most frequently. From the data:

[tex]\[ \ \begin{align*} \text{Score of 25 has 14 students} \\ \text{Score of 50 has 23 students} \\ \text{Score of 75 has 19 students} \\ \text{Score of 100 has 8 students} \end{align*} \][/tex]

The highest frequency is 23 students who scored 50. Thus, the mode is 50.

### Step 5: Assess if the Data is Skewed Right

Data is typically considered skewed right if the right side (higher value end) has a longer tail and fewer frequencies in higher values compared to lower values.

Given:
- Maximum score is 100
- Mode score is 50
- Average score is around 58.203125

Since the mode (50) is lower than the average (58.203125) and there are fewer students scoring higher values (only 8 students scored 100), this suggests the data is indeed skewed right.

### Conclusion

Having calculated and analyzed the data:
- The total number of students is 64.
- The total score is 3725.
- The average score per student is approximately 58.2.
- The mode is 50.
- The data is skewed right.

Thus, the true statements are:
- The average score earned per student is 58.2.
- The mode is 50.
- The data is skewed right.

Therefore, "all of the statistics provided are true" is the correct statement.
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