Statistics

Question 1

Explain Dispersion!

And what is range?

Answer 1

It is die Streuung, so it explains how spread out the data is. A value near 0 means it is rarely spread out, whereas a high value means it is spread out vastly.

Range is the difference between the smallest and the largest elements. Range 0 means max and min have the same values

Question 2

Covariance? What is it?

Answer 2

It is the paired analogue to variance. While the variance is measured by its vary to the mean, the covariance is calculated by how the two variables vary in tandem from their means. Yet it can be hard to interpret the number so the correlation is normally used.

Question 3

Explain Correlation, its range, explain the pearson correlation coefficient formula and explain how to calculate it.

Answer 3

1 is a perfect positive correlation
0 is no correlation (the values don’t seem linked at all)
-1 is a perfect negative correlation

1. Obtain a data sample with the values of x-variable and y-variable.
2. Calculate the means (averages) x̅ for the x-variable and ȳ for the y-variable.
3. For the x-variable, subtract the mean from each value of the x-variable (let’s call this new variable “a”). Do the same for the y-variable (let’s call this variable “b”).
4. Multiply each a-value by the corresponding b-value and find the sum of these multiplications (the final value is the numerator in the formula).
5. Square each a-value and calculate the sum of the result. Same with b.
6. Find the square root of the value obtained in the previous step (this is the denominator in the formula).
7. Divide the value obtained in step 4 by the value obtained in step 7.

Question 4

Explain the Simpsons Paradox! Give an Example!

Answer 4

You can take two completely different conclusion out of the data(p.e. treatment is effective/is not effective), depending on where you divide the data.

we know that men earn more than women. Now we have200m and 200w appling for jobs in Psychology and Engineering. At Psychology, 140 women and 60 men apply. At Engerineering, 140 men and 60 women. The quote of admission is at 50% in both cases. At the end, the men will earn more, even though both genders have been treated equally. Why? Women tend to go into professions where the wages are smaller. Thus, you cannot say that women earn less as an argument that they get treated worse.

Conclusion: Know your data!