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, 35, 38, 32, 31. a) Find the median. b) Find the mean. c) Find the range. d) Find the standard deviation. e) Find the z-score for child 4. f) Find the z-score for child 5. g) For child 1, find the standardized score with a mean of 59 and SD of 10. h) For child 3, find the standardized score with a mean of 59 and SD of 10.

Answer 1

31, 35, 38, 32, 31

A) Median

arrange in increasing order

31 31 32 35 38

Median = middle most value = 32

B) Mean(u) = sum of all observations/ total observations

= 31+35+38+32+31 /5

= 33.4

C) Range = Maximum - Minimum

= 38 - 31

= 7

D)

Now lets take difference of  31 31 32 35 38 and mean u = 33.4

-2.4 -2.4 -1.4 1.6 4.6

now square the terms and add them

5.76 5.76 1.96 2.56 21.16

S.D =standard deviation = (5.76+ 5.76+ 1.96 +2.56 +21.16) / 4

= 3.04

E) Z score for child #4

x = Marks = 32

Z score = (X - u )/ S.D

= (32 - 33.4) / 3.04

=-0.46

F) Z score for child #5

x = Marks = 31

Z score = (X - u )/ S.D

= (31 - 33.4) / 3.04

= -0.789

g)

X = 31

u = 59 , SD = 10

Z score = (X - u )/ S.D

= -12 /10

= -1.2

h)

X = 38

u = 59 , SD = 10

Z score = (X - u )/ S.D

= -21 /10

= -2.1