Summary of Applications of Histograms

Monitoring Your Readiness

To effectively plan and use your time wisely, it helps to think about what you know and do not know. For each of the following, rate how confident you are that you can successfully do that skill. Use the following descriptions to rate yourself:

5—I am extremely confident I can do this task.

4—I am somewhat confident I can do this task.

3—I am not sure how confident I am.

2—I am not very confident I can do this task.

1—I am definitely not confident I can do this task.

Skills Needed for Applications of Histograms: Forming Connections

Skill or Concept: I can . . . Questions to check your understanding Rating from 1 to 5
Use technology to make a histogram of a quantitative variable. 1
Use a histogram to answer questions about the distribution of a quantitative variable. 2
Describe the shape of a distribution. 3
Describe the center and spread of a distribution. 4, 5
Identify if there are outliers in a distribution. 6
Match the description of a distribution to the graphical display. 7

Now use the ratings to get ready for your next in-class activity. If your rating is a 3 or below, you should get help with the material before moving forward. Remember, your instructor is going to assume that you are confident with the material and will not take class time to answer questions about it.

Ways to get help:

  • See your instructor before class for help.
  • Ask your instructor for on-campus resources.
  • Set up a study group with classmates so you can help each other.
  • Work with a tutor.

Essential Concepts

  • The description of a distribution of a quantitative variable can be identified using the shape, center, spread, and presence of outliers.
  • The shape of a distribution has two parts to consider, overall pattern (left-skewed, symmetric, and right-skewed) and the number of peaks (unimodal, bimodal, and multimodal). Uniform is included in the modality, but represents no peaks present in the distribution.
  • The center describes the point in the distribution where about half of the observations are below it and half are above it. The use of histograms help you approximate this value.
  • When describing the spread of a distribution that is left-skewed, right-skewed, or has outliers, it can be misleading to only rely on the range to measure spread, since it is influenced by skewness and outliers. In this case, the range may make the spread appear to be larger than it is for a vast majority of the data.

Study Tips: Evidence-based strategies for learning

  • Create a mnemonic for the characteristics of the distribution of a quantitative variable. For example, SOCS can help you remember Spread, Outliers, Center, and Shape. If it helps to recall them in the order they were presented in the text, use SCSO for Shape, Center, Spread, Outliers. (Mnemonics & Symbols)
  • Each of the characteristics of a quantitative distribution is described further by characteristics. Use flashcards to test your recall of what these are and which of the four major characteristics it belongs to. (Retrieval practice, Mnemonics & Symbols)
    • Shape consists of skew and modality
      • Skewed Left: the tail is extending to the Lower values, the values to the Left on the horizontal axis.
      • Skewed Right: the tail is extending to the Rising values, the values to the Right on the horizontal axis.
      • Modality: unimodal, bimodal, multimodal, uniform (use little sketches to remember these)
    • Center: the location of the middle, with half the data values above and half below.
    • Spread: minimum and maximum values, the difference is the range.
    • Outliers: unusual observations
    • Note that the definitions of center and outliers will become more precise in following sections.

Foundational Knowledge

Glossary

bimodal
two prominent peaks in the distribution.
center
a measure that describes where the middle of the distribution is. The center is a number that describes a typical value. For example, one way to think about center is that it could be the point in the distribution where about half of the observations are below it and half are above it.
left-skewed
the visual distribution where the left side has a longer tail.
maximum
the largest observation or value.

minimum
the smallest observation or value.

modality
the number of peaks in the description of the shape in a data set.
multimodal
three or more prominent peaks in the distribution.
outlier
unusual observations that are outside the general pattern of the distribution.
range
the difference between the minimum and maximum values in the data set.
right-skewed
the visual distribution where the right side has a longer tail.
shape
the overall pattern (left skewed, right skewed, symmetric) and the number of peaks (unimodal, bimodal, multimodal, uniform).
skew/skewness
a visual difference from symmetry in a data set.

spread
a measure of how far apart the data are. In this lesson, the range is used to measure spread. The range is the difference between the maximum value and minimum value.

symmetric
the left and right sides of the distribution (closely) mirror each other. If you drew a vertical line down the center of the distribution and folded the distribution in half, the left and right sides would closely match one another.
uniform
no prominent peaks in the distribution.

unimodal
one prominent peak in the distribution.

 

My Skills Checklist:

  • I can use common statistical language to describe a distribution based on what is observed from a graphical display.
  • I can identify the description of a distribution of a quantitative variable including the shape, center, spread, and presence of outliers.
  • I can identify a range as a misleading representation of spread for distributions that are skewed and/or contain outliers.
  • I can describe the distribution of a quantitative variable using the shape, center, spread, and presence of outliers.
  • I can identify an appropriate representation of the spread based on the shape of the distribution and presence of outliers.

Check mark list on clipboard

Topic Complete – now test your understanding in the Self-Check.