Let's analyze the information given about the scores in relation to the selected statements:
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The median is 78 points.
- This means when the scores are arranged in ascending order, the middle score (third student) is 78.
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The mean is 82 points.
- This means the total score of all 5 students is: \[ \text{Mean} = \frac{\text{Total Score}}{\text{Number of Students}} \] \[ 82 = \frac{\text{Total Score}}{5} \] Therefore, the Total Score = \( 82 \times 5 = 410 \) points.
Now let's evaluate the statements:
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At least one student scored an 82 on the assessment.
- Not necessarily true. The mean being 82 does not imply that any individual score must be 82.
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The scores ranged from 74 to 86.
- This cannot be determined to be true without additional information about the actual scores.
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The 5 students' combined points on this assessment was 410 points.
- This is true, as calculated above.
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At least one student scored a 78 on the assessment.
- This is also true because the median is defined as the middle score, meaning at least one student must have scored 78.
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Most students scored 82 or higher on the assessment.
- This is not necessarily true. With a mean of 82, it’s possible to have a distribution where not most students scored 82 or higher.
Based on this analysis, the two true statements are:
- The 5 students' combined points on this assessment was 410 points.
- At least one student scored a 78 on the assessment.