Question

A graduate student obtains data from a sample of children with ADHD. The data represent level of activity where higher scores indicate more activity and are as follows: 31, 25, 38, 32, 39. a) Find the median. b) Find the mean. c) Find the range. d) Find the standard deviation. e) Find the z-score for child 3. f) Find the z-score for child 4. g) For child 2, find the standardized score with a mean of 62 and SD of 11. h) For child 1, find the standardized score with a mean of 62 and SD of 11.

Answer 1

a) Median :

The ascending Order of values are

25

31

32

38

39

Median is middle value of the data i.e. 32

b) Mean = (Sum of all value) / Number of values = 165/ 5 = 33

c) Minimum value = 25

Maximum value = 39

Range = 39-25 = 14

d)

From the given data

	Data(Xi)	(xi-33)^2
	25	64
	31	4
	32	1
	38	25
	39	36
Total :	165	130

Sample variance S^2 = 130/4 = 32.5

SD = Sqrt (32.5) = 5.701

e)

Z score of child 3 = (38 - 32) / 5.701 = 1.05245

f)

Z score of child 4 = (32-32) / 5.701 = 0

g) Z = (25 - 62) / 11 = -3.3636

h) Z = (31 - 62) / 11 = -2.8182