Answer:
1. 13.98
2. 14.47
Step-by-step explanation:
The question is on sample standard deviation and population standard deviation
<u>Arrange the data in increasing order</u>
12,14, 16,16,17,19,21,26,35,37,42,43,45,46,56
n=15
<u>Find the mean of the data set</u>
<u />
![mean = (12+14+ 16+16+17+19+21+26+35+37+42+43+45+46+56)/15](https://tex.z-dn.net/?f=mean%20%3D%20%2812%2B14%2B%2016%2B16%2B17%2B19%2B21%2B26%2B35%2B37%2B42%2B43%2B45%2B46%2B56%29%2F15)
mean= 29.67 ⇒30
<u>Find the deviations</u>
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
<u>Find squares of deviations</u>
= 324, 256, 196, 196, 169, 121, 81, 16, 25, 49, 144, 196, 225, 256, 676
<u>Find sum of squares of deviations</u>
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