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1.4 Measures of Central Tendency

It is a form of Numerical Summaries, along with Dispersion and Variance.

Mean

Measure of the center location of a data set.
- μ: Population (Total data set)
- ͞x: Sample (An extract of selected data from the full data set)
- It is also the point estimator for μ.
- For Excel: =AVERAGE()

Median

  • The middle value or the average of the 2 middle values.
  • It is preferred when there are outliers and the mean is affected.

Mode

The most repeating value (or multiple values that repeat the same number of times).
- Unimodal: When there is 1 mode value.
- Bimodal: When there are 2 mode values.
- Multimodal: When there are more than 2 mode values.
- For Excel: MODE.SNGL / MODE.MULT

Percentiles

Describes the spread of the data from the smallest to largest value.
- p% of observations are lesser than the p percentile, 100-p% of observations are greater than the p percentile.
- P percentile shows how much percent of the values are lesser than or greater than p. image

  • Arrange in ascending order and compute the index.
  • If the value of Lp is an integer, it can directly be read from the data.
  • If the value of Lp is not an integer, use linear interpolation.
    For Excel: PERCENTILE.EXE(array, k)

Quartiles

  • Specific percentiles. All steps for computing percentiles can be directly applied to quartiles.
  • Quartiles are broken into 25, 50, 75, and 100 percentiles.
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