X 23, Median=28, mode 31 for a particular distribution of 25 scores. It was subsequently found that a scoring mistake had been made: one score of 43 should have been a 34.

Question

i) What is the correct value for X?
ii) How would the Median and mode be affected by this error?

Answer 1

i) The correct value for X can be found by subtracting 43 (the incorrect score) and adding 34 (the correct score):

Correct X = (X + 43 - 34) / 25 = 23
(X + 9) / 25 = 23
X + 9 = 23 * 25
X = 575 - 9
X = 566

So, the correct value for X is 566.

ii) The median and mode would not be affected by this error. The median is the middle value of the data set when arranged in ascending order, and the mode is the most frequently occurring value. Since the incorrect score of 43 is not used in calculating the median or mode, correcting this mistake would not change the values of the median and mode.