An ordinary fair die was rolled 100 times...

Question

An ordinary fair die was rolled 100 times. The results were summarised in a frequency table and the mean score was calculated to be 3.46. It was later discovered that the frequencies, 15 and 20, of two consecutive scores had been swapped.

Find the least and greatest possible value of the true mean score.

Please show your process.

Answer 1

Denote the two consecutive scores for that the frequencies were swapped as x and x+1.

If score x has frequency 15 and score x+1 has frequency 20, their part in the mean is

(15x + 20(x+1))/100 = (35x +20)/100

If score x has frequency 20 and score x+1 has frequency 15, their part in the mean is

(20x + 15(x+1))/100 = (35x +15)/100

So, because of swapping the error of the mean equals 5/100 (the mean is underestimated or overestimated).

The true mean score is easier 3.41 or 3.51.