Answer:
Standard deviation = 14.064
Step-by-step explanation:
We are given the following data;
X X - [tex]Xbar[/tex] [tex](X-Xbar)^{2}[/tex]
20 20 - 46 = -26 676
23 23 - 46 = - 23 529
32 32 - 46 = -14 196
36 36 - 46 = -10 100
41 41 - 46 = -5 25
43 43 - 46 = -3 9
44 44 - 46 = -2 4
45 45 - 46 = -1 1
47 47 - 46 = 1 1
54 54 - 46 = 8 64
55 55 - 46 = 9 81
59 59 - 46 = 13 169
61 61 - 46 = 15 225
63 63 - 46 = 17 289
66 66 - 46 = 20 400
[tex]\sum(X-Xbar)^{2}[/tex] = 2769
Firstly we will calculate Mean, [tex]Xbar[/tex] = [tex]\frac{\sum X}{n}[/tex]
[tex]Xbar = \frac{20+ 23+ 32+ 36+ 41+ 43+ 44+ 45+ 47+ 54+ 55+ 59+ 61+ 63+ 66}{15}[/tex] = 45.93 ≈ 46
Now, Standard deviation formula is given by;
s = [tex]\sqrt{\frac{ \sum(X-Xbar)^{2}}{n-1}}[/tex] = [tex]\sqrt{\frac{ 2769}{15-1}}[/tex] = 14.064 .
