f6 maths

a) For the set of data10, 10, 11, 12,13, 16, find the mode, median, mean and the range.

The mode = 10
The median = (11 + 12)/2 = 11.5
The mean = (10 + 10 + 11 + 12 + 13 + 16)/6 = 12
The range = 16 - 10 = 6


b) Four unknown dataare combined with the six data in (a) to form a set of ten data.
i) Find the least andthe greatest possible values of the median of the combined set of ten data.

If the median of the combined set of ten data reached the least possible value,all of the four unknown data should be not greater than 10. The ten data are:
x, x, x, x, 10, 10, 11, 12, 13, 16
The median = (10 + 10)/2 = 10

If the median of the combined set of ten data reached the greatest possiblevalue, all of the four unknown data should be not less than 16. The ten dataare:
10, 10, 11, 12, 13, 16, x, x, x, x
The median = (13 + 16)/2 = 14.5


ii) If the mean of thefour unknown datais 11, find the mean of the combined set of the ten data.

The mean of the combined set of ten data
= (11*4 + 12*6)/10
= 11.6