From everyday questions to specialized queries, IDNLearn.com has the answers. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.

Find the standard deviation of the data set (36, 18, 12, 10, 9). Round all calculations to the nearest tenth. Please Help!!!!​

Sagot :

Answer:

The standard deviation of the data set is [tex]\sigma=10[/tex]

Step-by-step explanation:

The formula for standard deviation is [tex]\sigma=\sqrt{\frac{1}{N}\sum_{n=1}^{\infty}(x_i-\mu)^2 }[/tex] where you are basically taking the mean of the data set ([tex]\mu[/tex]), find the mean of the squared differences from the observed values and mean ([tex](x_i-\mu)^2[/tex]), and square root the result:

Mean:

[tex]\mu=\frac{36+18+12+10+9}{5}=\frac{85}{5}=17[/tex]

Average of squared differences (variance):

[tex]\frac{1}{N}\sum_{n=1}^{\infty}(x_i-\mu)^2=\frac{(36-17)^2+(18-17)^2+(12-17)^2+(10-17)^2+(9-17)^2}{5}=\frac{500}{5}=100[/tex]

Standard deviation:

[tex]\sigma=\sqrt{100}=10[/tex]

This means that the standard deviation of the data set is 10, which tells us that the values of the data set, on average, are separated by 10.