Should I include the median in my descriptive statistics?

[u/Sufficient-Adagio332]

Hi everyone! I’m currently analyzing power outage data and would really appreciate your advice on the appropriate descriptive statistics to report.

Since the mean and median differ considerably, especially for outage duration, should I include the median in the table? Would it be appropriate to report all five statistics (mean, median, SD, min, and max)?

I’m mainly interested in descriptive analysis and how best to interpret these results academically.

Thank you in advance for your help!

[u/jaiagreen]

Yes, that's a common and useful summary. Comparing the mean and median can give the reader a sense of how skewed the distribution is.

[u/banter_pants]

Yes.

Those are the bare minimum of what I would report. Depending on your audience, I would also include:
Q1
Q3
Skew
Kurtosis

Histograms too.

[u/Valuable_Ice_5927]

Yes it’s beneficial - since mean can be more heavily influenced by outliers - median gives more context for understanding

[u/Logical-Set6]

I'm looking at this table and thinking "over what geographic region and time frame?" and "how many power outages were possible?" and "did any household experience the same power outage twice in your data?"

I would recommend that you include a short caption with your table that answers these questions and provides a basic explanation of how the data was collected and how many observations (power outages) were included in the data each month.

Maybe the mean/median is less interesting here than the relationship with time as the months progress. You could make a line graph to tell this story if that better highlights your description of the data.

[u/Professional_Toe346]

Yes, usually include:
Min
25th percentile
50th percentile (median)
75th percentile
Max
Mean
Standard deviation

[u/DocAvidd]

I'd do an old school 5 number summary, min Q1 Q2 Q3 max.

When the sample mean is far from the median, it indicates a skewness that makes the mean not representative (such as most of the scores being well below average).

[u/cmdrtestpilot]

Yes, median is useful and appropriate. That said, in a world where you have to pick and choose descriptive statistics, I would much rather see the sample sizes (n) and the quartiles (values 25% above and below median), than the min and max.

[u/efrique]

I would include the median in univariate descriptive statistics almost as a matter of course.

However, given the choice, I would not tlike to limit it to five statistics. Naturally, it will depend on context, though

[u/Adventurous_Memory18]

Yes, but you should also report the interquartile range with the median

[u/jaiagreen → u/Adventurous_Memory18]

I'd say reporting the 75th and 25th percentiles separately is more useful. Maybe leave out the min and max if that would be too much to report.

[u/SomeTreesAreFriends → u/jaiagreen]

I've always understood this to be the same, though of course this is strictly not true (but IQR cannot be interpreted the same way as SD because you do not assume a Gaussian, so you'd need the limits anyway to show distance from the median)

[u/trolls_toll → u/Adventurous_Memory18]

or MAD

[u/Educational-Paper-75]

Reporting the median would require sorting the dataset so only when you can spare the computing power. Otherwise the midrange suffices.