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Find the population standard deviation (σ not S) for the data set: {75,80,90,95,75,85,55,80,90,95}
Round your answer to the nearest 10th.

Respuesta :

1. Find the mean (arithmetic mean) of the numbers:

[tex] \frac{75+80+90+95+75+85+55+80+90+95}{10}=82 [/tex]

2. Find the differences of each number to the mean, and calculate the square of each of these differences :

82-75=7,           7^2=49
82-80=2            2^2=4
90-82=8            8^2=64
95-82=13         13^2=169
82-75=7            7^2=49
85-82=3             3^2=9
82-55=27           27^2=729
82-80=2              2^2=4
90-82=8             8^2=64
95-82=13           13^2=169

3. Calculate the mean of the differences (the Variance):

[tex] \frac{49+4+64+169+49+9+729+4+64+169}{10}= 131.2[/tex]

4. Standart deviation is the root of the variance = [tex] \sqrt{131.2} =11.5[/tex]

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