Heidi and John are teachers teaching similar classes and both gave their classes an exam. Here are the summaries for the exam scores:Heidi's class:Mean 75Median 78Standard Deviation 3John's class:Mean 75Median 65Standard Deviation 12 Which of the following statements is most correct? Group of answer choicesJohn's class had some students who received very low scores, exactly 50% of his students scored less than or equal to 75%, and the scores were quite varied when compared to Heidi's class scores.John's class likely had some outlier scores that were very high, exactly 50% of his students scored less than or equal to 65%, and the scores were quite varied when compared to Heidi's class scores.The scores in John's class were more consistent than the scores in Heidi's class.Since the median is higher than the mean in Heidi's class, there were likely some outlier scores that were very high.John's class likely had some outlier scores that were very high and thus the mean would be the best measure of center for his data set.
Question
Heidi and John are teachers teaching similar classes and both gave their classes an exam. Here are the summaries for the exam scores:Heidi's class:Mean 75Median 78Standard Deviation 3John's class:Mean 75Median 65Standard Deviation 12 Which of the following statements is most correct? Group of answer choicesJohn's class had some students who received very low scores, exactly 50% of his students scored less than or equal to 75%, and the scores were quite varied when compared to Heidi's class scores.John's class likely had some outlier scores that were very high, exactly 50% of his students scored less than or equal to 65%, and the scores were quite varied when compared to Heidi's class scores.The scores in John's class were more consistent than the scores in Heidi's class.Since the median is higher than the mean in Heidi's class, there were likely some outlier scores that were very high.John's class likely had some outlier scores that were very high and thus the mean would be the best measure of center for his data set.
Solution
The most correct statement is: "John's class likely had some outlier scores that were very high, exactly 50% of his students scored less than or equal to 65%, and the scores were quite varied when compared to Heidi's class scores."
Here's why:
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John's class likely had some outlier scores that were very high: This can be inferred from the fact that the mean (75) is significantly higher than the median (65). This suggests that there are some high scores pulling the mean up.
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Exactly 50% of his students scored less than or equal to 65%: This is the definition of the median - 50% of scores fall below this value.
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The scores were quite varied when compared to Heidi's class scores: This is indicated by the standard deviation, which is a measure of variability. John's class has a standard deviation of 12, compared to Heidi's class which has a standard deviation of 3. This means that the scores in John's class were more spread out or varied than those in Heidi's class.
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