Question

The following data represents the numbers of books checked out from the college library during one semester by a random sample of students. 2 7 5 13 4 0 10 5 6 8

a. How large is the sample? b. What is the total number of books checked out by all the students in the sample? c. Find the sample mean. d. Find the sample variance. e. Find the sample standard deviation.

Answer 1

Solution:

a ) The large sample is = 13

b ) The total number of books checked out by all the students = 10

x	x2
2	4
7	49
5	25
13	169
4	16
0	0
10	100
5	25
6	36
8	64
∑x=60	∑x2=488

c ) The sample meanˉx=∑xn

=2+7+5+13+4+0+10+5+6+8/10

=60/10

=6


d ) The Sample Variance S2=∑x2-(∑x)2nn-1

=488-(60)210/9

=488-360/9

=128/9

=14.2222


e ) The Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√488-(60)210/9

=√488-360/9

=√128/9

=√14.2222

=3.7712