Mr. Burke teaches GED classes in the evenings to young adults. His students recently took the English GED Test. Their scores are summarized in the box plot below.

Question

Based on the data in the box plot, determine if each conclusion is valid or invalid.
Valid Invalid
More than 50% of the students scored above 60.
The range of the scores is 50.
25% of the students scored 80 or above.
The mean test score was 60.

Answer 1

To assess the validity of each conclusion based on the box plot, we need to briefly understand what the box plot represents. A box plot provides a visual summary of the distribution of the data, including the minimum, first quartile (Q1), median, third quartile (Q3), and maximum scores.

Here’s how to evaluate each conclusion:

1. More than 50% of the students scored above 60.
   Validity: Invalid
   The box plot shows the median (the line inside the box), which represents the 50th percentile. If the median score is at or below 60, then 50% or more of the students scored at or below 60.

2. The range of the scores is 50.
   Validity: Valid
   The range is calculated by subtracting the minimum score from the maximum score. If the minimum score is 30 and the maximum score is 80, then the range is indeed 80 - 30 = 50.

3. 25% of the students scored 80 or above.
   Validity: Valid
   In a box plot, the upper quartile (Q3) represents the 75th percentile, and thus 25% of the students scored above Q3. If the maximum score of 80 is at Q3 or above, then indeed 25% of the students scored 80 or above.

4. The mean test score was 60.
   Validity: Invalid
   A box plot does not provide information on the mean; it only shows the median and quartiles. Therefore, we cannot determine whether the mean is 60 without additional data.

In summary:

• More than 50% of the students scored above 60: Invalid
• The range of the scores is 50: Valid
• 25% of the students scored 80 or above: Valid
• The mean test score was 60: Invalid