Drawing conclusions from data involves interpreting tables, dot plots, histograms, and box plots to describe distributions in context, including typical values, variability, clusters, gaps, and possible outliers. Comparisons between data sets should use appropriate measures such as mean or median and range, interquartile range, or mean absolute deviation, recognizing that a typical value does not describe every observation. Conclusions at this level are descriptive or informal, not formal statistical inferences, confidence claims, or causal explanations.
To draw a conclusion from data, describe:
The table shows how many books 12 students read in one month.
| Books read | Number of students |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 3 |
| 5 | 2 |
| 10 | 1 |
Write the data in order:
There are 12 values, so the median is the mean of the 6th and 7th values:
A typical student read about 3 or 4 books.
The range is the greatest value minus the least value:
The number of books read varies from 1 to 10 books, so the data have a fairly wide spread.
Most of the data are between 2 and 5 books, so this is a cluster. There is a gap from 6 to 9 books. The value of 10 is far from most of the other values, so it may be an unusual value.
Most students read between 2 and 5 books in one month, with a typical student reading about 3 or 4 books. The amounts varied from 1 to 10 books, and the student who read 10 books may be unusual compared with the rest.
Remember that a typical value describes the center of the data, not every student.
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