Question

#1 Compute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.)

−1, 9, 9, 2, 11

variance
standard deviation

#2 Compute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.)

−8, 3, 6, 8, 0, 6

variance
standard deviation

#3 Compute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.)

2.8, −3.2, 2.5, −0.2, −0.2

variance
standard deviation

Please answer all three questions. Thank you very much

Answer 1

Solution:

1 ) Given that

x	x2
-1	1
9	81
9	81
2	4
11	121
∑x=30	∑x2=288

Sample Variance S2=∑x2-(∑x)2nn-1

=288-(30)25/4

=288-180/4

=108/4

=27
Sample Variance = 27
Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√288-(30)25/4

=√288-180/4

=√108/4

=√27

=5.1962

Sample Standard deviation = 5.20

2 ) Given that

x	x2
-8	64
3	9
6	36
8	64
0	0
6	36
∑x=15	∑x2=209

Sample Variance S2=∑x2-(∑x)2nn-1

=209-(15)26/5

=209-37.5/5

=171.5/5

=34.3
Sample Variance = 34.3

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

=√209-(15)26/5

=√209-37.5/5

=√171.5/5

=√34.3

=5.8566

Sample Standard deviation = 5.86

3 ) Given that

x	x2
2.8	7.84
-3.2	10.24
2.5	6.25
-0.2	0.04
-0.2	0.04
∑x=1.7	∑x2=24.41

Sample Variance S2=∑x2-(∑x)2nn-1

=24.41-(1.7)25/4

=24.41-0.578/4

=23.832/4

=5.958

Sample Variance =5.96
Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√24.41-(1.7)25/4

=√24.41-0.578/4

=√23.832/4

=√5.958

=2.4409

Sample Standard deviation =2.44