Answer:
1. 13.98
2. 14.47
Step-by-step explanation:
The question is on sample standard deviation and population standard deviation
Arrange the data in increasing order
12,14, 16,16,17,19,21,26,35,37,42,43,45,46,56
n=15
Find the mean of the data set
[tex]mean = (12+14+ 16+16+17+19+21+26+35+37+42+43+45+46+56)/15[/tex]
mean= 29.67 ⇒30
Find the deviations
You subtract the value of mean from each of the data set given
Deviations= -18, -16, -14, -14, -13,-11, -9,-4,5,7,12,13,15,16,26
Find squares of deviations
= 324, 256, 196, 196, 169, 121, 81, 16, 25, 49, 144, 196, 225, 256, 676
Find sum of squares of deviations
[tex]324+ 256+ 196+ 196+ 169+ 121+ 81+ 16+ 25+ 49+ 144+ 196+ 225+ 256+ 676 = 2930[/tex]
1. Treating the data set to represent an entire population then;
Variance= sum of squares of deviation/number of data set
Variance= 2930/15 = 195.33
Population standard deviation = √195.33 = 13.98
2. Treating the data set as a sample , the number of data set is reduced by one.i.e n= 15-1= 14
Sample Variance=2930/14 =209.29
sample standard deviation= √209.29 = 14.47
