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, 32, 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 3.


f) Find the z-score for child 1.


g) For child 4, find the standardized score with a mean of 52 and variance of 121.00.


h) For child 2, find the standardized score with a mean of 52 and variance of 121.00.

Answer 1

a) For the given sample the mean the median is calculated as the middle value, the data set is 31, 32, 38, 32, 31, hence the sample size is 5 so the Median lies at 3rd position when arranged in ascending order as 31, 31, 32, 32, 38 thus the median is 32.

b) The mean for the sample is calculated as:

Mean = (31 + 31 + 32 + 32 + 38)/5
= 164/5
Mean = 32.8

c) The range is calculated as Maximum -Minimum.

So, range = 38-31 =7.

d) The standard deviation for the sample is calculated as:

Standard Deviation σ = √(1/5 - 1) x ((31 - 32.8)² + ( 31 - 32.8)² + ( 32 - 32.8)² + ( 32 - 32.8)² + ( 38 - 32.8)²)
= √(1/4) x ((-1.8)² + (-1.8)² + (-0.8)² + (-0.8)² + (5.2)²)
= √(0.25) x ((3.24) + (3.24) + (0.64) + (0.64) + (27.04))
= √(0.25) x (34.8)
= √(8.7)
= 2.9496

e) The Z score is calculated as:

Where the 3rd child score is X =38 so, the Z score is:

f) The Z score for child 1 whoses score is 31 is calculated as:

Note: As per Cheeg guidelines first 4 subparts has to be answered but i have as many as possible.