The Measures and definitions for central tendency allow you to find the middle or average of a data set. The three most commonly used measures of central tendency are the median, mode, and mean.
- Mode is the most common value.
- Median is the middle number in an ordinal dataset.
- The sum of all the values divided by the total value.
When performing descriptive statistics, it is essential to understand the definition of central tendency and the distribution of your data.
Distributions and central tendencies
A dataset is a distribution of n numbers of scores or values.
A normal distribution data structure ensures that data is evenly distributed and there is no skew. The majority of values are concentrated in a central area, with values decreasing as they move further from that center. Normal distributions have the mean, median, and mode the same.
Distributions with skew
In skewed distributions more values fall on the one side than the other. The mean, median, and mode are all different. The tail on one side is longer and more spread with less scores at the ends. This tail indicates which side you are on.
A positively skewed distribution has a cluster with lower scores and a spread-out tail to the right. A negatively skewed distribution has a cluster with higher scores and a spread tail to the left.
The value is most often found in the dataset. You can have one, two, or all three modes.
You can find the mode by sorting your data numerically or categorically, and then selecting the most frequent response.
The median value in a dataset is exactly the middle value when the order is from low to high.
It is easier to use simple formulas when working with large datasets. There are many ways to determine the median value of a dataset. It all depends on how many values you have.
What does that mean?
By definition the central tendency is the arithmetic means of a data set (which may differ from the geometric mean) and refers to the sum of all the values divided by the total value. Because all values are included in the calculation, it is the most common measure of central tendencies.
What is the best time to use the median, mean or mode?
Because they each have strengths and weaknesses, the three main measures of central tendencies are best combined. Depending on the measurement level, only one or two of these measures may apply to your data.
- This mode can be used at any level of measurement but is most useful for ordinal and nominal levels.
- Only data that can be ordered can be used to calculate the median, which is ordinal, interval, and ratio levels of measurement.
- Because it requires equal spacing between adjacent scores or values in the scale, the mean cannot be used for interval and ratio measurements.