The mean gave us a cold average of your digital servitude, but averages can be deceiving, skewed by extreme bouts of doomscrolling or rare moments of digital abstinence. Enter the median. The median is the true middle value in a dataset when that data is ordered from least to greatest. It's less susceptible to outliers – those days you spent 16 hours online or, conversely, the glorious 30 minutes you managed to stay offline.
To find the median, you must first arrange your screen time data points in ascending order. Then, you simply locate the middle value. If you have an odd number of data points, the median is the single value exactly in the middle. If you have an even number, the median is the average of the two middle values.
The median offers a slightly more honest snapshot of your typical digital engagement, uncolored by the extremes. It represents the point where half of your screen time measurements fall below it, and half fall above. It's the statistical equivalent of the lukewarm center of your digital existence.
Let's sort our sample screen time data and find the median.
Unlike the mean, calculating the median requires you to first order your data points from smallest to largest. Let our sorted data be $X_{\text{sorted}} = \{x_{(1)}, x_{(2)}, \dots, x_{(n)}\}$, where $x_{(1)}$ is the smallest value and $x_{(n)}$ is the largest.
Using our example data $X = \{3, 5, 4, 6, 7, 5, 4\}$, the sorted data is: $X_{\text{sorted}} = \{3, 4, 4, 5, 5, 6, 7\}$.
In the visualization above, the data points are shown arranged in order along a horizontal line.
The method for finding the median depends on whether you have an odd or even number of data points ($n$).
If $n$ is odd, the median is the single middle value. Its position in the sorted list is $\frac{n+1}{2}$.
If $n$ is even, the median is the average of the two middle values. Their positions are $\frac{n}{2}$ and $\frac{n}{2} + 1$.
In our example, $n=7$, which is odd. The position of the median is $\frac{7+1}{2} = 4$. The 4th value in the sorted list $\{3, 4, 4, \underline{5}, 5, 6, 7\}$ is 5.
The visualization highlights the data point(s) corresponding to the median.
The median is the value found in Step 2. It divides the dataset into two equal halves.
Median $= x_{(\frac{n+1}{2})}$ if $n$ is odd.
Median $= \frac{x_{(\frac{n}{2})} + x_{(\frac{n}{2} + 1)}}{2}$ if $n$ is even.
For our example data, the Median is 5 hours. This means on half the days, you spent 5 hours or less on screen, and on half the days, you spent 5 hours or more. It's a more robust measure of the "center" of your data than the mean, less influenced by those outlier days that might inflate or deflate your average misery.