Graph Interpretation

This recognition and recall practice is based on a very simple graphs in California Youth Authority's slide presentation on changing characteristics of youthful offenders.

• Age at First Commitment to CYA

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1. Name the variable or variables in this graph, and tell whether they are measured as nominal, ordinal, or interval.

   One plausible response:

   The primary variable is age, measured in years. Therefore, interval.

2. What does the 16.8 on the y-axis mean?

   One plausible response:

   The 16.8 represents sixteen years and eight tenths of a year in age. If you follow the line associated with 16.8 across the bar graph, you will be able to see that all those above the line are older than 16 years and eight tenths of a year. And all those below the line are younger than 16 years and eight tenths of a year.

3. Isn't 16.8 an awkward number to describe? Why do you think it was used?

   One plausible response:

   Eight tenths of a year is 8/10 x 12 months = 96/10 months = 9.6 months. It might have been a lot clear to say 16 years and almost 10 months, or round off (collapse data) and say 17 years.

   I think it was used because it was at this upper level of the scale that most of the important results were shown. Remember the issue was the increasingly early ages at which young people are being committed to the CYA. In order to draw the readers attention to the top of the graph, notice that the y-axis does not go down to zero, and that each year is broken into smaller segments. Each year is broken into 5 segments, or 1/5 of a year.

   It thus becomes a presentation issue of whether we want a neat graph with 16.8 years of age, or whether we want to give years and months. Another problem is that tenths can't be broken into twelfths easily. Perhaps the easiest thing to have done would have been to give years and months. This won't bother a sophisticated reader; but it may bother someone not used to such calculations. Again, this probably will depend on the audience.

4. How can you tell that age is inversely related to the progression of time?

   One plausible response:

   At a glance you should be able to tell by the fact that the imaginary line you could draw over the tops of each bar would slant down from left to right. Look at the scatter gram in a correlation. r is negative (-r) when the scatter gram slants down from left to right. r is positive (+r) when the scattergram slants up from left to right.

   But an inverse relationship here is exactly what you would expect. That fits the CYA concern that they are receiving a younger population.

5. Can you find the graph in the CYA series that says the population is also more violent than in previous years?

   One plausible response:

   Yes. Changes in the number and type of commitment offenses. (1986-1997)

   How many young offenders committed violent crimes in 1997?
   Approximately 1400.

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