For the following sample of scores, 1, 1, 2, 2, 2, 2, 4, a. ...

[Diane]

For the following sample of scores, 1, 1, 2, 2, 2, 2, 4,
 
  a. find the mean, median, and mode.
  b. if a new individual with a score of X = 2 is added to the sample, what happens to the values for the mean, the median, and the mode?
  c. if the score X = 4 in the original distribution is changed to X = 11, what happens to the values for the mean, the median, and the mode?

Question 2

A sample of n = 6 scores has a mean of M = 8 . One new score is added to the sample, and the new mean is computed to be M = 7 . What is the value of the score that was added to the sample?
 
  What will be an ideal response?

[Liddy]

Answer to Question 1

a. The mean, median, and mode are all equal to 2.
b. Adding a score of X = 2 does not change the mean, the median, or the mode.
c. Changing X = 4 to X = 11 causes the mean to change to M = 3 . The median and the mode are still equal to 2.

Answer to Question 2

The original sample had n = 6 scores. X = 48 . After the new score is added, there are n = 7 scores with X = 49 . Because the sum increased by 1 point, the new score must be X = 1.