The following ten scores were obtained on a 20-point quiz: 4,5,8,9,11,13,15,18,18,and 20.The teacher computed the usual descriptive measures of center (central tendency)and variability (dispersion)for these data,and then discovered an error was made.One of the 18s should have been a 16.Which of the following measures,calculated on the corrected data,would change from the original computation?
A)median
B)arithmetic mean
C)range
D)geometric mean

Question

Quizplus · Accepted Answer

The arithmetic mean would change because it takes into account the value of every score, and changing one score would change the overall average. The median would not change because it is simply the middle value and is not influenced by extreme scores like the 16 or 20. The range would not change because it is simply the difference between the highest and lowest scores, and changing one score would not affect that difference. The geometric mean is not commonly used for this type of data, and would not change anyway because it involves multiplying the scores together and taking the nth root, not affected by a single changed score.

The Following Ten Scores Were Obtained on a 20-Point Quiz