Megoldás - Statistics

Divide the sum by the number of terms:

Sum
$$37 324$$
Number of terms
$$6$$

$$x̄=\frac{18662}{3}=6220,667$$

The mean equals $$6220,667$$

Arrange the numbers in ascending order:
4,24,144,864,5184,31104

Count the number of terms:
There are (6) terms

Because there is an even number of terms, identify the middle two terms:
4,24,144,864,5184,31104

Find the value that is halfway between the middle two terms by adding them together and dividing by 2:
$$\left(144+864\right)/2=1008/2=504$$

The median equals 504

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

The highest value equals 31 104
The lowest value equals 4

$$31104-4=31100$$

The range equals 31 100

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 6220,667

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:
$$38646944 444+38398677 778+36925877 778+28693877 778+1074677 778+619180277 778=762920333 334$$
Number of terms:
$$6$$
Number of terms minus 1:
5

Variance:
$$\frac{762920333 334}{5}=152584066 667$$

The sample variance ($$s^2$$) equals 152584066,667

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: $$s^2=152584066,667$$

Find the square root:
$$s=\sqrt{\left(152584066,667\right)}=12352492$$

The standard deviation ($$s$$) equals 12352 492