Question

question 13
find the standard deviation. round to one more place than the data.
17, 9, 14, 15, 8, 5, 6, 17, 17
a 4.7
b 5.3
c 1.5
d 5.0

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{17 + 9+14 + 15+8 + 5+6 + 17+17}{9}=\frac{108}{9} = 12$

Step2: Calculate the squared differences

$(17 - 12)^2=25$, $(9 - 12)^2 = 9$, $(14 - 12)^2=4$, $(15 - 12)^2 = 9$, $(8 - 12)^2=16$, $(5 - 12)^2 = 49$, $(6 - 12)^2=36$, $(17 - 12)^2=25$, $(17 - 12)^2=25$

Step3: Calculate the variance

The variance $s^{2}=\frac{25+9 + 4+9+16+49+36+25+25}{9}=\frac{198}{9}=22$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{22}\approx4.7$

Answer:

A. 4.7