Question

QUESTION 2

1. A professor grades a statistics test and records the grades. She computes the mean, median, standard deviation, and the interquartile range of the grades. Later, she decides to give 3 extra points to each student, and computes the mean, median, standard deviation, and the interquartile range of the new grades. Which of the parameters change between the two computations?

   A professor grades a statistics test and records the grades. She computes the mean, median, standard deviation, and the interquartile range of the grades. Later, she decides to give 3 extra points to each student, and computes the mean, median, standard deviation, and the interquartile range of the new grades. Which of the parameters change between the two computations?

   		Mean, median, and standard deviation
   		We cannot answer the question without knowing the whole dataset
   		Mean, median, and interquartile range
   		Mean and standard deviation
   		Mean and median

Answer 1

Answer: Mean and Median

Explanation:

Let us understand with the help of an example.

Let X denote the grades : (2,4,2.4,3,2,4,4,5,3.2)

So,

1st Quartile = 2.4

Median = 3.2

Mean = 3.289

3rd Quartile = 4

IQR = 4 - 2.4 = 1.6

Standard Deviation = 1.039765

Adding 3 points, we get x' = (5.0 7.0 5.4 6.0 5.0 7.0 7.0 8.0 6.2)

So,

1st Quartile = 5.4

Median = 6.2

Mean = 6.289

3rd Quartile = 7

IQR = 4 - 2.4 = 1.6

Standard Deviation = 1.039765

Therefore, Mean and Median changes, but IQR and Standard Deviations are same