TheJoyOfHack

For people who like to make things

A key aspect of good photography is exposure - the amount of light that enters the lens.  One of the most useful tools a digital cameras has to help you measure a photograph’s exposure is the histogram. In order to learn how to use it, you must first learn understand what a histogram is.

Let’s pretend I teach a class of 20 students. One day I decide to give the students a test in which they can score anywhere from 0 to 100 points.  After grading the tests I want to see how the population of students did.  So I graph the scores in a histogram. A histogram displays the distribution of measured values across a population.  Let’s make one now.

The following table lists my fictional students’ scores:

Alice       82
Bob         79
Chetan      88
Darla       94
Evan       100
Fatima      89
Gerard      96
Harry       43
Ibtissam    68
Jack        56
Kate        93
Labiba      70
Mary        76
Noreen      83
Ophelia     92
Pablo       63
Qazveen     84
Rick        89
Sophia      73
Taline      89

The first thing I do is make a bunch of ‘buckets’ of values into which each score should go.  The larger the bucket size the more scores it will have. The smaller the bucket size the fewer scores it will have.  I choose a bucket size of 5 points because that seems like a nice level of granularity.  5 points gives me the following 20 buckets:

0-5
6-10
11-15
16-20
21-25
26-30
31-35
36-40
41-45
46-50
51-55
56-60
61-65
66-70
71-75
76-80
81-85
86-90
91-95
96-100

I draw these buckets horizontally because that’s how histograms are almost always drawn:

| | | | | | | | | | | | | | | | | | | | |
0 5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 1
    0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0
                                        0

The next thing I do is go through the list of scores and put each score in its appropriate bucket.  I do this by marking an X in the appropriate bucket. Alice scored 82, so I mark an X in the bucket between 80 and 85.  Bob got 79, so I put an X in the bucket between 75 and 80.  When I’m done, the histogram looks like this:

                                  X
                                X X X
                            X X X X X X
                 X     X X X X X X X X X
| | | | | | | | | | | | | | | | | | | | |
0 5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 1
    0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0
                                        0

The x axis of this histogram has the ranges of values (scores) and the y axis represents the number of data points that have that value.

If you think about it, this histogram has less data than the original table did - It doesn’t map a student’s name to their score.  However, it does illustrate the distribution of the scores in a manner that isn’t obvious from the table: Looking at this histogram you can see that most students scored 75 or higher, and that more students scored in the 85-90 bucket than in any other bucket.  We call distributions that look like this ‘skewed to the right’ - most of the data points are towards the right end of the histogram.

Now that you know what histograms are, you’re ready to use them to take better photos.  I’ll cover that in Monday’s blog post.

References

Wikipedia entry on histograms.