Statistics How To

Measures of Position

Descriptive Statistics >

Measures of position give us a way to see where a certain data point or value falls in a sample or distribution. A measure can tell us whether a value is about the average, or whether it’s unusually high or low. Measures of position are used for quantitative data that falls on some numerical scale. Sometimes, measures can be applied to ordinal variables— those variables that have an order, like first, second…fiftieth.

Measures of position can also show how to values from different distributions or measurement scales compare. For example, a person’s height (measured in feet) and weight (measured in pounds) can be compared by converting the measurements to z-scores.

Common Measures of Position

  1. Box and Whiskers Plot,
  2. Deciles,
  3. Five Number Summary,
  4. Interquartile Range (IQR),
  5. Outliers,
  6. Percentiles,
  7. Quartiles,
  8. Standard scores (i.e. z-scores),
  9. Tukey’s upper hinge and lower hinge.

1. Box and Whiskers Plot

A box and whiskers plot shows the spread and center of data. It is a graphical representation of the five number summary: minimum, maximum, median, and the first and third quartiles.

2. Deciles

Deciles are similar to quartiles. But where quartiles split the data in four equal parts, deciles split the data into ten parts: The 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th and 100th percentiles.

3. Five Number Summary

The five number summary is an overview of your data. The statistics in the summary are the smallest value (minimum), the largest (maximum), the middle (median) and the first and third quartiles.

4. Interquartile Range (IQR)

The interquartile range tells you where the “middle fifty” is in a data set. While the range tells you where the beginning and end are in a set, the IQR shows you where the bulk of the “middling” values lie.

5. Outliers

Outliers are unusual values that fall outside of an expected range of values. For example, if you’re measuring IQ values of children, your statistics would be thrown off if Einstein and Stephen Hawking were in your class: their IQs would be outliers.

6. Percentiles

A percentile is a number where a certain percentage of scores fall below that number. For example, a 90th percentile marks the spot where 90% of values fall below that cut-off point.

7. Quartiles

Simply put, quartiles divide your data into quarters: the lowest quarter, two middle quarters, and a highest quarter.

8. Standard scores (i.e. z-scores)

Z-scoresare a way to compare results from a test to a “normal” population.

9. Tukey’s upper hinge and lower hinge

Tukey’s upper hinge and lower hinge are created when you split a data set into four pieces (with three hinges). As the median is included in this “splitting,” Tukey’s hinges are sometimes called inclusive quartiles.

References

Antonius, R. (2003). Interpreting Quantitative Data with SPSS. SAGE. Retrieved August 26, 2019 from: https://books.google.com/books?id=H1_mH0glk0IC
UF Biostatistics. Measures of Position. Retrieved August 26, 2019 from: https://bolt.mph.ufl.edu/6050-6052/unit-1/one-quantitative-variable-introduction/measures-of-position/

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Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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