Question

In a medical class of 147 students, the distribution of scores on a biochemistry final examination has a mean equal to 67, a median equal to 76, a mode equal to 80, a standard deviation equal to 5.5, and a variance equal to 30.25. Three students were unable to take the test on the scheduled date and were given a different form of the exam 1 week later. Which parameter is most likely to be the least biased estimator of central tendency for this distribution of biochemistry test scores? a. Mean b. Median c. Mode d. Standard deviation e. Variance

Answer 1

We know that mean, standard deviation, mode and variance are dependent on each data value present in the data set.

We know that mean = (sum of all values)/(total number of values). So, mean value will vary maximum with the test scores as it dependent on each individual test scores.

Standard deviation and variance are calculated using the mean value, so standard deviation and variance will vary similar to mean value.

Mode is the highest occurring data value or highest frequency data value, so mode can also change by 3 test scores which were given a different form of exam.

Median is calculated using the middle values, so median will be least biased because there is not much variation possible in the middle values of the data set.

So, correct answer is median or option B