Megoldás - Statistics

Divide the sum by the number of terms:

Sum
$$\frac{2057}{10}$$
Number of terms
$$5$$

$$x̄=\frac{2057}{50}=41,14$$

The mean equals $$41,14$$

Arrange the numbers in ascending order:
1,7,5,1,15,3,45,9,137,7

Count the number of terms:
There are (5) terms

Because there is an odd number of terms, the middle term is the median:
1,7,5,1,15,3,45,9,137,7

The median equals 15.3

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

The highest value equals 137,7
The lowest value equals 1,7

$$137,7-1,7=136$$

The range equals 136

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 41,14

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:
$$1555 514+1298 882+667 706+22 658+9323 834=12868 594$$
Number of terms:
$$5$$
Number of terms minus 1:
4

Variance:
$$\frac{12868 594}{4}=3217 148$$

The sample variance ($$s^2$$) equals 3217,148

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: $$s^2=3217,148$$

Find the square root:
$$s=\sqrt{\left(3217,148\right)}=56720$$

The standard deviation ($$s$$) equals 56,72