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skyluke89
The standard deviation of a set of data is given by
[tex]\sigma = \sqrt{ \frac{1}{N} \sum (x_i - \mu)^2} [/tex]
where
N is the number of data (in this case, N=5)
[tex]x_i[/tex] are the data
[tex]\mu[/tex] is the average value

Let's calculate the average value:
[tex]\mu = \frac{52.1+45.5+51+48.8+43.6}{5}=48.2 [/tex]

And now we can apply the formula to calculate the standard deviation:
[tex]\sigma = \sqrt{ \frac{1}{5} \sum ( x_i - 48.2 )^2} =[/tex]
[tex]= \sqrt{ \frac{1}{5} ( (3.9)^2 + (-2.7)^2 + (2.8)^2 + (0.6)^2 + (-4.6)^2 ) } =[/tex]
[tex]= \sqrt{ \frac{1}{5} (51.86) } =3.2[/tex]

Answer:

Standard deviation is 3.2.

Step-by-step explanation:

Given data is,

52.1, 45.5, 51, 48.8, 43.6,

Let x represents the data points,

Now, mean of the data is,

[tex]\mu = \frac{52.1 + 45.5 + 51 + 48.8 + 43.6}{5}=48.2[/tex]

Population size, N = 5,

Hence, the standard deviation of the following data set is,

[tex]\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu )^2[/tex]

[tex]=\sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i-48.2 )^2[/tex]

[tex]=\sqrt{\frac{1}{5} (15.21+7.29+7.84+0.36+21.16)}[/tex]

[tex]=\sqrt{10.372}[/tex]

[tex]=3.2205589577[/tex]

[tex]\approx 3.2[/tex]

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