Question

A group of high school students was surveyed about their use of various drugs, including alcohol. Asked how frequently they had been drunk in the previous six months, the students responded:

4 2 0 2 1 3 0 7 5 3

Calculate the (a) range, (b) inter-quartile range, and (c) variance and standard deviation for these self-report scores. Please graph it on a normal distribution as well.

Answer 1

X	(X - X̄)²
4	1.69
2	0.49
0	7.29
2	0.49
1	2.89
3	0.09
0	7.290
7	18.490
5	5.290
3	0.090

	X	(X - X̄)²
total sum	27	44.10
n	10	10

a) range=max-min =    7-0=   7.000

b)

quartile , Q1 = 0.25(n+1)th value=   2.75th value of sorted data=   0.75
      
Quartile , Q3 = 0.75(n+1)th value=   8.25th value of sorted data=   4.25
      
IQR = Q3-Q1 =    4.25-0.75=   3.5

c)

sample variance =    Σ(X - X̄)²/(n-1)=   44.1/9=   4.900
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √(44.1/9)=   2.214