Question

write a table to show your steps for calculating the standard deviation and then use your table to calculate the standard deviation of the values listed:

10, 11, 12, 10.5, 11.25, 12.25, 10

Answer 1

Answer:

The standard deviation for the given data set is 1.65.

Step-by-step explanation:

The Standard Deviation is defined as

$\sigma =\sqrt{\frac{\Sigma (x_{i} -\mu)^{2} }{N-1} }$

Where $\sigma$ is the standard deviation, $\mu$ is the mean and $N$ is the total number of data.

So, first, we need to find the mean of the data set.

$\mu = \frac{10+11+12+10.5+11.25+12.25+10}{7} =11$

Now, we have to subtract each data with the mean to then elevate the differnece to the square power.

$10-11 = -1 \implies (-1)^{2}=1\\ 11-11 = 0 \\12-11 = 1 \implies 1^{2}=1\\ 10.5-11 = -0.5 \implies (-0.5)^{2} =0.25\\11.25 - 11 = 0.25 \imples (1.25)^{2}=0.0625\\12.25 - 11 = 1.25 \implies (1.25)^{2}=1.5625\\10-11 = -1 \implies (-1)^{2}=1$

Then, we sum all these results.

$\Sigma (x_{i}- \mu )^{2}=1+0+1+0.25+0.0625+1.5625+1=16.278$

Next, we divide the sum by $N-1=7-1=6$

$\frac{\Sigma (x_{i}-\mu )^{2} }{N-1}=\frac{16.278}{6} \approx 2.713$

Finally, we apply the square root.

$\sigma = \sqrt{2.713} \approx 1.65$

Therefore, the standard deviation for the given data set is 1.65.