Estimates

Probability of success for binary data. It's pretty much considered the same as the sample mean here.

$$ p = \frac{\text{number of successes}}{n} $$

Independent Continuous Measures include the sample mean

$$ \text{The sample mean (often represented as } \bar{x} \text{) is calculated as follows:} $$

$$

\bar{X} = \frac{1}{n} \sum_{i=1}^{n} X_i

$$

The median is the single middle value of the sorted $𝑋_i, … ,𝑋_𝑛$ for $𝑛$ odd and the average of the two middle values for $𝑛$ even.

Terms to keep an eye out for

Proportion (Essentially the Mean or Success Probability for binary data)

Sample Mean (Referred for Continuous Data)

<aside> 💡 The mean is weak to outliers. The median is very robust against outliers. Equations that inherit the mean’s definition predominantly suffer from outliers as well.

</aside>

<aside> 💡 Quantiles and medians are considered Non-Parametric because they do not assume that the data follows a specific distribution.

</aside>

Using the median is favorable when the distribution suffers from outliers or when the data distribution is unknown (It is much safer to try out both, and even better to first understand the data distribution).

Variance and inter-quartile range

How to Calculate the IQR:

1. Arrange the Data: First, arrange your data in ascending order.
2. Find the Median: The median splits the data into two halves. If the number of data points is odd, the median is the middle data point. If even, it is the average of the two middle numbers.
3. Find the Quartiles:
   • Q1 (Lower Quartile): This is the median of the lower half of the data (excluding the median if the number of data points is odd).
   • Q3 (Upper Quartile): This is the median of the upper half of the data (again, excluding the median if the number of data points is odd).