A histogram represents the distribution of numerical data by grouping values into consecutive intervals and using adjoining bars whose heights show the frequency in each interval. Interpretation includes determining approximate counts and ranges, identifying the center, spread, clusters, gaps, peaks, and possible unusual values, while understanding that a bar represents an interval rather than a single value and that the graph does not reveal individual data values.
A histogram shows how numerical data are grouped into intervals. Each adjoining bar represents one interval, and the height of the bar tells how many data values are in that interval.
Example: A histogram shows the number of minutes students spent reading.
| Reading time (minutes) | Bar height |
|---|---|
Read the histogram step by step:
Find the frequency for an interval.
The bar for reaches , so about students read for between and minutes.
Find the interval with the greatest frequency.
The tallest bar is , so this is the peak. Reading times in this interval were most common.
Describe the center.
Most of the data are between and minutes. Therefore, a typical reading time is around minutes.
Describe the spread.
The data extend from the interval to the interval. So the reading times cover approximately to minutes.
Look for clusters and gaps.
The bars from form a main cluster. The interval has no bar, creating a gap.
Look for a possible unusual value.
Only student is in the interval. This may be an unusually large reading time compared with the main cluster.
Remember that a bar represents a whole interval, not one exact value. The bar for tells us that students are in that range, but it does not tell us their individual reading times.
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