Statistics

$$r = x_{d}-x_{m}$$

r - sample width
x_m - minimum sample value
x_d - maximum sample value

Find It is known that:

$$c = \frac{x_{d}+x_{m}}{2}$$

c - sample center
x_m - minimum sample value
x_d - maximum sample value

Find It is known that:

Relative frequency

$$p_{k} = \frac{m_{k}}{n}$$

p_k - relative frequency
m_k - frequency of event k occurence
n - number of sample elements

Find It is known that:

Calculate 'p_k'

$$x_{v} = \frac{x_1+x_2+x3}{n}$$

x_v - sample mean (average)
x1, x2, x3 ... - sample values
n - number of sample elements

Find It is known that:

Calculate 'x_v'

$$x_{v} = \frac{x_1\cdot m_1+x_2\cdot m_2+x3\cdot m3}{n}$$

x_v - sample mean (average)
x1, x2, x3 ... - sample values
m1, m2, m3 ... - frequencies of sample elements
n - number of sample elements

Find It is known that:

Calculate 'x_v'

Sample variance (dispersion)

$$s^{2} = \frac{(x_1-x_{v})^{2}+(x_2-x_{v})^{2}+(x3-x_{v})^{2}}{n-1}$$

s^2 - sample variance (dispersion)
x1, x2, x3 ... - sample values
x_v - sample mean (average)
n - number of sample elements

Find It is known that:

Sample variance (dispersion)

$$s^{2} = \frac{(x_1-x_{v})^{2}\cdot m_1+(x_2-x_{v})^{2}\cdot m_2+(x3-x_{v})^{2}\cdot m3}{n-1}$$

s^2 - sample variance (dispersion)
x1, x2, x3 ... - sample values
m1, m2, m3 ... - frequencies of sample elements
x_v - sample mean (average)
n - number of sample elements

Find It is known that:

Sample variance (dispersion)

$$s^{2} = x_1^{2}\cdot p_1+x_2^{2}\cdot p_2+x3^{2}\cdot p3-x_{v}^{2}$$

s^2 - sample variance (dispersion)
x1, x2, x3 ... - sample values
p1, p2, p3 ... - relative frequencies of sample elements
x_v - sample mean (average)

Find It is known that:

Standard deviation

$$s = \sqrt {s^{2}}$$

s - standard deviation
s^2 - sample variance (dispersion)

Find It is known that: