Question

On Professor Hardtack's last cost accounting exam, the mean score was 71, the median was 77, and the mode was 81. (a) Check the appropriate choice of the distribution, based on the statistics given. a. The distribution should be skewed to the left because the mean is less than the median. b. The distribution should be skewed to the left because the standard deviation is less than the median. c. The distribution should be skewed to the right because the mean is less than the median. d. The distribution should be skewed to the right because the coefficient of variance is less than the median. (b) Select the factor that might cause the distribution to be like this. (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.) a. Many students did not study for the exam b. No students scored a C c. Few students did not study for the exam d. Most students scored a C or higher

Answer 1

Answer:

A. The correct answer is A. The distribution should be skewed to the left because the mean is less than the median.

B. The correct answers are:

C. Few students did not study for the exam

D. Most students scored a C or higher.

Step-by-step explanation:

A. Let's recall that skewness is "a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined."

According to this definition, we have that on Professor Hardtack's last cost accounting exam, the mean score was less than the median and less than the mode, therefore, using the Pearson’s first coefficient of skewness, the distribution is negatively skewed or left-skewed.

The correct answer is A. The distribution should be skewed to the left because the mean is less than the median.

B. If  the mean score was 71, the median was 77, and the mode was 81, therefore, we have that:

The majority of the students scored equal to or higher than 71 (C) and just a little amount of students scored less than 71 because they did not study for the exam. Therefore, the correct options are:

C. Few students did not study for the exam

D. Most students scored a C or higher.

Answer 2

Answer:

A. The distribution should be skewed to the left because the mean is less than the median.

B. Most students scored a C or higher.

Step-by-step explanation:

A. Since mean<median<mode, we have a negative skewness and hence the distribution is skewed to the left.

B. Since the mean score is 71 and the modal score is 81, it is expected that a 'C' should be the lowest grade most students will have.