8E Summarizing Data Study Guide

Key Vocabulary

Summarize — to describe the important features of a data set in a short way. (resumir)

Center — the middle or typical value of a data set (mean or median). (centro)

Spread — how far apart the data values are (range or MAD). (dispersión)

Shape — the overall pattern of the data (symmetric, skewed left, or skewed right). (forma)

Cluster — a group of data points that are close together. (grupo)

Gap — an empty space in the data where no values appear. (brecha)

Peak — the highest point or most frequent value in a data display. (pico)

1 Describe the CENTER — What is the mean? What is the median? This tells you the "typical" value.
2 Describe the SPREAD — What is the range? What is the MAD? This tells you how varied the data is.
3 Describe the SHAPE — Is the data symmetric (balanced on both sides), skewed left (tail goes left), or skewed right (tail goes right)?
4 Note any special features — Are there clusters, gaps, peaks, or outliers?

Symmetric
Data is balanced on both sides of the center. Mean and median are close together.

      *
    * * *
  * * * * *
  |---|---|---|
  Low Mid High

Skewed Right
Most data is on the left, with a long tail to the right. Mean > Median.

  *
  * *
  * * *
  * * * *   *
  |---|---|---|
  Low Mid High

Skewed Left
Most data is on the right, with a long tail to the left. Mean < Median.

          *
        * *
      * * *
  *   * * *
  |---|---|---|
  Low Mid High

To summarize data, you need BOTH center AND spread. Just saying "the mean is 15" is not enough.
Use median when there are outliers. The mean is pulled toward outliers, but the median is not.
"Symmetric" does NOT mean exactly equal on both sides — it means approximately balanced.
Look at the data display first before calculating numbers. The shape tells a story!

1. Which measure tells you the "typical" or middle value of a data set?
Type "center" or "spread".

2. Range and MAD describe the _____ of a data set (how varied the data is).
Type "center" or "spread".

3. If most data is on the left side with a long tail stretching right, the data is:
Type "symmetric", "skewed right", or "skewed left".

4. A data set has values: 10, 12, 11, 50, 13, 12. The 50 is much bigger than the others. What is this value called?