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Identify outliers informally

An outlier is a data value that lies noticeably far from the main cluster or overall pattern of a data set, as seen in lists, dot plots, or other simple graphs. Identifying one requires considering the distribution and context; an outlier is not automatically the greatest or least value and may represent an unusual but valid observation or a recording error, while potentially affecting measures of center and variability.

Detailed Explanation: Identify outliers informally

An outlier is a data value that is noticeably far from the rest of the data. To identify one:

  1. Look at the values in order.
  2. Find the main cluster, or group, of values close together.
  3. Look for a value separated from that cluster by a large gap.
  4. Decide whether that value is unusual in the context.

Example: The numbers of books read by 8 students in one month are

2, 3, 3, 4, 4, 5, 5, 152,\ 3,\ 3,\ 4,\ 4,\ 5,\ 5,\ 15

Step 1: Find the main cluster.
Most of the values are between 22 and 55. These numbers are close together, so they form the main cluster.

Step 2: Look for a value far from the cluster.
The value 1515 is much greater than the other values. There is a large gap between 55 and 1515.

Step 3: Identify the outlier.
The outlier is

15\boxed{15}

It means one student read many more books than the rest. The outlier is not automatically the greatest or least value; it is the value that is noticeably separated from the main pattern.

Learn by doing: Identify outliers informally

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    Statistics - Quartiles - Data Set and Point to Is Outlier

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