Megoldás - Statisztika

Divide the sum by the number of terms:

Sum
$$285$$
Number of terms
$$8$$

$$x̄=\frac{285}{8}=35,625$$

The mean equals $$35,625$$

Arrange the numbers in ascending order:
1,8,9,17,26,43,69,112

Count the number of terms:
There are (8) terms

Because there is an even number of terms, identify the middle two terms:
1,8,9,17,26,43,69,112

Find the value that is halfway between the middle two terms by adding them together and dividing by 2:
$$\left(17+26\right)/2=43/2=21,5$$

The median equals 21,5

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

The highest value equals 112
The lowest value equals 1

$$112-1=111$$

The range equals 111

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 35,625

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:
$$1198 891+763 141+708 891+346 891+92 641+54 391+1113 891+5833 141=10111 878$$
Number of terms:
$$8$$
Number of terms minus 1:
7

Variance:
$$\frac{10111 878}{7}=1444 554$$

The sample variance ($$s^2$$) equals 1444,554

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: $$s^2=1444,554$$

Find the square root:
$$s=\sqrt{\left(1444,554\right)}=38007$$

The standard deviation ($$s$$) equals 38 007