A science teacher gives a test with 15 questions. This teacher is a hard grader.
The teacher assigns points in the following manner: a correct answer = +1 point, an incorrect answer = -1 point, no answer = 0 points.
So scores on the test could range from +15 to -15. The teacher’s assistant calculates the standard deviation for scores on the test and reports SD = -2.3.
What do we know?
a. The standard deviation was calculated incorrectly.
b. Most students received negative scores.
c. Most students scored below the mean.
d. There is an outlier that has a negative value close to -15.
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To determine what we know based on the information given, let's analyze the options one by one:
a. The standard deviation was calculated incorrectly.
This option suggests that the calculation of the standard deviation (-2.3) is incorrect. However, without additional information, we cannot definitively conclude that the standard deviation was calculated incorrectly based solely on the given values.
b. Most students received negative scores.
The given information does not directly indicate that most students received negative scores. The range of scores is from +15 to -15, and it is not mentioned whether there are more positive or negative scores overall.
c. Most students scored below the mean.
Since the standard deviation is reported to be -2.3, it indicates that the scores are relatively dispersed with negative deviations. This suggests that there may be more students who scored below the mean. Therefore, option c is a plausible answer.
d. There is an outlier that has a negative value close to -15.
The standard deviation value of -2.3 does not directly provide information about the presence or nature of an outlier. It signifies the dispersion of scores rather than the position of specific values. Therefore, option d is not supported by the given information.
Based on the analysis, the most plausible answer is:
c. Most students scored below the mean.