Welcome back to the dissection table of your digital life. We've mapped the cage; now let's weigh the chains. The first tool in our statistical arsenal is the mean, also known as the average. It's the single number that attempts to summarize a whole set of data – in this case, the grim tally of your daily screen time.
Calculating the mean is brutally simple. You just add up all the numbers (your screen time for each day) and divide by how many numbers you have (the number of days you measured). The result is a stark, emotionless representation of your typical digital consumption. It doesn't care about that one day you were offline, or the weekend binge; it just gives you the cold, hard average.
This number is what the algorithms often use as a baseline. They know your average engagement, and they work tirelessly to keep you there, or ideally, push that average ever higher. It's a key metric in the system designed to commodify your attention. Let's see how this works with some sample data – perhaps a week of your own (hypothetical) screen time.
Observe the data points below, and see where the calculated mean falls.
A time series is a sequence of data points collected at specific time intervals. We can represent it as $Y = \{y_t \mid t \in T\}$, where $y_t$ is the value of the variable at time $t$, and $T$ is the set of time points.
For example, tracking your "relationship happiness score" (on a scale of 1 to 10) weekly for 10 weeks:
$Y = \{8, 7, 6, 7, 5, 4, 6, 5, 4, 3\}$
Here, $t$ could be the week number (1 to 10), and $y_t$ is the score for that week.
In the visualization above, the horizontal axis represents time (Week), and the vertical axis represents the "Happiness Score". Each data point is plotted according to its time and value.
The most common way to visualize a time series is using a line plot. The data points $(t, y_t)$ are plotted on a Cartesian coordinate system, and consecutive points are connected by lines.
This line plot allows us to visually inspect the behavior of the time series over time, revealing patterns that might not be obvious from just looking at the raw numbers.
In our visualization, the blue line connects the red data points, showing the trajectory of the hypothetical happiness score over the 10 weeks.
The crucial aspect of a time series is the order of the data points. The value at time $t$ is often dependent on the values at previous times ($t-1, t-2$, etc.). This time dependence is what makes time series analysis different from analyzing independent data points.
Understanding this dependence is key to identifying trends, seasonality, and ultimately, attempting to forecast future values – or predict the next downturn in your relationship drama.