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.
