London’s 17 passengers per bus – why averages don’t always tell you what you most need to know

Undercover economist, Tim Harford, has this in the Financial Times today (29 November 2014):

“… the average London bus has only 17 people riding on it.”

(You may have to log in but the FT does give limited access at no cost.)

A report to the London Assembly’s Transport Committee in October 2013 confirms the figure on page 13 – though the reference is to a committee transcript from December 2012.

Plenty of room for all, you might think. That is if you’re not a commuter waiting in the rain as crowded bus after crowded bus goes by.

As Harford points out – and you’ve probably guessed – it’s an issue of averages. This comes about from having a few very full buses and lots with much lower or no occupancy.

Usually this sort of ‘odd’ result comes from taking the mean – add all the numbers up and divide by how many you’ve got. The lots of small numbers outweigh the few big ones.

But it can happen with the median – the number in the middle when you line them up in order.

And even the mode might not be useful – the single most frequent number.

How might this be? Say a bus records the following occupancy over 21 trips:

45, 39, 17, 10, 7, 4, 8, 7, 2, 0, 7, 7, 9, 1, 11, 8, 7, 15, 35, 37, 4

The mean occupancy is a little over 13 passengers (13.3). The median is 8. The mode is 7.

That all sounds comfortable. Of the 21 trips, 17 have occupancy of 17 passengers or less. But if you’re on one of the four trips when the bus is full or nearly so, that is what matters. You might decide to give up on bus travel, fed up with day after day of uncomfortable rides. If others do the same it’s easy to see how a bus company has to cut services because of a drop in earnings.

So, averages can be useful. But they might not tell the story that you’re most interested in.

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