Respuesta :
Answer:
3.16
Step-by-step explanation:
Mean:
(12+14+5+13+11)/5
11
Sum of squares:
12²+14²+5²+13²+11²
655
Variance = 655/5 - 11²
= 10
sd = sqrt(10)
3.16227766
A standard deviation (or) is a measure of how distributed the data is with respect to the mean. The standard deviation of the given data points is 3.2.
What is a standard deviation?
A standard deviation (or) is a measure of how distributed the data is with respect to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.
[tex]\sigma = \sqrt {\dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}}[/tex]
If it's a sample, we divide by n-1 instead of n.
To find the standard deviation, we need to find the mean of the given da points,
[tex]Mean = \dfrac{12+14+5+13+11}{5} = 11[/tex]
Now, the difference of every data point from the mean will be,
|12-11|² = 1
|14-11|² = 9
|5-11|² = 36
|13-11|² = 4
|11-11|² = 0
Now, the standard deviation can be written as,
[tex]{\rm Standard\ deviation}, \sigma = \sqrt{\dfrac{\sum|x-\bar x|^2}{n}}[/tex]
[tex]= \sqrt{\dfrac{1+9+36+4+0}{5}}\\\\=\sqrt{\dfrac{50}{5}} \\\\= \sqrt{10}\\\\=3.16227 \approx 3.2[/tex]
Hence, the standard deviation of the given data points is 3.2.
Learn more about Standard Deviation:
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