Various stats questions with explanations

Solution Preview

---

1) Describe how scale impacts the interpretation of a graph

The scale is on the y axis of a graph, and could play a huge role in how your visually examine your results.

For example, imagine you are trying to see what percentage of people like candidate X for mayor. The results are that 15% of people like him.

If your scale on the y-axis goes from 0 to 100%, then the representation of 15% will look tiny.
HOWEVER, if you have scale that goes from 0 to 20%, the 15% will look huge, and actually take up 75% of the scale.

If you were to visually eyeball the data without closely looking at the scale, you would think that candidate X is well loved in the second scenario, while he is disliked in the first.

2) Name the lowest number of a statistically significant sample size

According to the central limit theorem, in order to gain statistical significance, you need to have 30 people in a sample to have statistical significance.

3) State the statistically appropriate percentage total of displays

Total percentage of displays would be number of displays/total observations

4) Explain how mean, median, and mode are applied to categorical and numerical data
Let us first go over what categorical and numerical data is.

Numerical data is anything that has to do with number. Categorical data is when a person is dealing with categories or terms.

For example: numerical data would be: how old are you?
Categorical data would be: What is your favorite flavor of ice cream.

With numerical data, you can take the data collected, and apply stats to it right away,
Mean is the average of the numbers
Median is the middle number
Mode is the most common number.

Now with categorical data, mode is a good tool to use. We can't exactly say that the mean ice cream flavor is vanilla. Instead, what a researcher needs to do is assign a numerical value to each category. For example, vanilla would be coded as '1' chocolate as '2' and strawberry would be a '3'.

You can then see the mode of this data, which number if the most common, (2 for example which would be chocolate).
The other 2 measures (mean and median do not work for categorical data).

5) List the characteristics of a normal bell curve
- The highest point on the bell curve is the mean of the data, which is the exact center of the bell curve
- The mean is equal to the median in a normal bell curve
- On each side of the mean, the bell curve is symmetrical
- The bell curve could extend to infinity on either end
- The sum of the area under the curve is equal to 1
- It follows the 'Empirical rule', where 68% of the population falls within 1 standard deviation of the mean, 95% of the population falls within 2 standard deviations, and 99.7% fall within 3 standard ...