Question

I have 2 populations of people (only 3 people in each) and I give them a memory test with 20 items and get the number of words they can recall.   For the first data set the number of items recalled is 10,13,and 16 and for the second dataset the scores are 9,12, and 15.

A.   What would be the most appropriate measure of central tendency to use for both data sets.   Compute that number and describe the results and conclusion you would reach based on that number. (5)

B.   Compute the 3 primary measures of dispersion for each population.   What conclusion did you reach? (15)

D.   If I had 20 people for the population in data set 2 provide with a rationale which measure of dispersion would be inappropriate to use. (5)

Answer 1

Deciphering the mean would be an appropriate measure of central tendency. The mean is found by adding the data and dividing by the number of items. The mean for the first set is therefore 39/3 which is 13. Similarly the result for the second set of data is 35/3 which is 11.6. The mean of the first set of data is greater than that of the second which means that more is recalled in the first assessment. This can be related to the fact that immediate recall is considered better than later recall.

1. Range: The range of data set 1 is 6 and the range of data set 2 is 6 as well. The range for both the sets is therefore the same.

2. Standard deviation for set 1: 2.44 (using the formula), standard deviation for set 2: 2.44, The standard deviation is therefore the same.

3. Median for set 1 is 13 and set 2 is 12.

The range and SD for both set of data is the same where as the median differs, wherein the first set's median is greater than the second.

D. Finding standard deviation seems a suitable choice for population of 20.