Megoldás - Statisztika

Divide the sum by the number of terms:

Sum
$$\frac{212201}{25}$$
Number of terms
$$4$$

$$x̄=\frac{212201}{100}=2122,01$$

The mean equals $$2122,01$$

Arrange the numbers in ascending order:
7,64,76,4,764,7640

Count the number of terms:
There are (4) terms

Because there is an even number of terms, identify the middle two terms:
7,64,76,4,764,7640

Find the value that is halfway between the middle two terms by adding them together and dividing by 2:
$$\left(76,4+764\right)/2=840,4/2=420,2$$

The median equals 420,2

To find the range, subtract the lowest value from the highest value.

The highest value equals 7 640
The lowest value equals 7,64

$$7640-7,64=7632,36$$

The range equals 7632,36

To find the sample variance, find the difference between each term and the mean, square the results, add together all of the squared results, and divide the sum by the number of terms minus 1.

The mean equals 2122,01

To get the squared differences, subtract the mean from each term and square the result:

To get the sample variance, add together the squared differences and divide their sum by the number of terms minus 1

Sum:
$$30448213 640+1844191 160+4184520 272+4470560 497=40947485 569$$
Number of terms:
$$4$$
Number of terms minus 1:
3

Variance:
$$\frac{40947485 569}{3}=13649161 856$$

The sample variance ($$s^2$$) equals 13649161,856

The standard deviation of the sample equals the square root of the sample variance. This is why the variance is usually represented by a squared variable.

Variance: $$s^2=13649161,856$$

Find the square root:
$$s=\sqrt{\left(13649161,856\right)}=3694477$$

The standard deviation ($$s$$) equals 3694 477