Question

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?

- The standard deviation was calculated incorrectly.
- Most students received negative scores.
- Most students scored below the mean.
- There is an outlier that has a negative value close to -15.

Answer 1

Answer: The standard deviation was calculated incorrectly.

Explanation:

• The standard deviation measures the dispersion of the data values from the mean value.

It cannot be negative , because it is the square root of the variance .

We add all squared deviations from the data points away from the mean and (then divide it by the number of data values) to evaluate variance.

Since , any squared number cannot give a negative result.

⇒ Standard deviation cannot be negative.

⇒The standard deviation was calculated incorrectly.

Rest other things (given in options) can not be interpreted on the basis of given information.