Question

Suppose you ask 4 people in a psychiatry [there are 150 patients in the psychiatry altogether] how often they hear voices from another planet per day; these are the results: (1, 3, 3, 13)

a) Compute mean, median and mode. Do you compute the sample or the population mean? (4 points)

b) Compute the variance and the standard deviation! (2 points)

c) Is the mean an appropriate measure for central tendency? Justify your answer in one or two sentences!

Answer 1

a) The mean of the sample is 5

The median of the sample is 3

The mode of the sample is 3

We have computed a sample mean based on the observations of the 4 individuals in the sample. The population mean would be the average number of times the 150 people hear voices in a particular day.

b) The variance is of the sample is given as:

= 29.33

The standard deviation is the sigma which is 5.42

c) The mean is much higher than the sample median and mode. This is due to the high 4th value of the sample. Mean is highly affeccted by extreme values whereas the median and the mode take into account the middle value as well as the most occurring values in the sample. So in this case of the small sample the mean seems to be not the most appropriate measure of the central tendency here. However, with large data mean will be more appropriate than edian and mode.