Measures of central tendency include descriptive statistics including the mean, median and
mode that are used to describe what the average person or response in a particular study is
like.
It is important as a research consumer to understand how these statistics are calculated
and used to summarize and organize information in a study.
Before talking about these measures of central tendency, it is important to know what a normal
distribution is.
The best measure of central tendency depends on a number of things including weather data
has a normal distribution or not.
The theoretical concept of a normal distribution is covered in more depth in another video,
but simply put it is the idea that when data are gathered from interval or ratio level
measures and plotted on a graph it will resemble a normal curve.
The three measures of central tendency described in this video would all fall at the same midline
point on a normal distribution curve.
However, if data are not normally distributed certain measures may be better than others.
The appropriateness of each measure is also influenced by the level of measurement used
in the study.
Throughout this video I will have examples of how to calculate the mean, median and mode
on the screen.
These examples will use the data I made up for a fake study about hours students spend
watching online videos and reading for studying purposes.
In statistics, mean is synonymous with the average.
Whether it is true or not you could try remembering that the average girl can be mean when they
want to be.
Or, if you can remember what the other two are so you can figure this one out through
the process of elimination.
You may remember how to calculate averages from math class.
To calculate the mean or average of a group of numbers, first add all the numbers.
Then, divide by the number of values.
Many programs automatically calculate averages for you.
However, it is still important to know how they are calculated in order to understand
how they work.
The mean or average is the most common, best known and most widely used measure to describe
the center of a frequency distribution.
The mean is influenced by all data in a Study.
For this reason, it works best for symmetrical distributions of data where there are no outliers
or extremes.
However, the larger the data set the smaller the influence of any extreme scores will be.
The mean is the most commonly use measure because it is considered the most reliable
measure of central tendency when making inferences from a sample population.
However, it is only appropriate for interval and ratio level data.
The Median is the value in the middle of a set of data.
One way to remember that median means middle is to try associating it with the word medium.
Median and medium sound sort of similar.
They also both start with the letters MED.
A medium pizza or a medium coffee is typically the size in the middle range at a store.
To calculate the median you need to find out the point at which 50% of the values are higher
and 50% of the values are lower.
To calculate it, first you need to arrange the numbers in order from lowest to highest.
Then, count to determine if there is an odd or even number of values.
If there is an odd number of values just pick the value in the middle of the range -- the
one with the same number of values above and below it.
If there is an even number of values simply divide the two numbers in the middle by 2.
Unlike the Mean, the mode is not influenced by extreme values in a data set.
Therefore, it is a good measure to use when distributions are not symmetrical.
If a researcher is working with data that are not normally distributed and wants to
know what the typical score is the median is likely the best measure to use.
In this situation both the mean and median would likely be reported.
The median is limited because it is not algebraically defined.
Instead it is simply the point in the middle of the data set.
While it is useful for ordinal, interval and ratio levels of measurement it cannot be used
for nominal data.
The Mode is the most frequent value, number or category in a set of data.
One way to remember this definition is that Mode sounds like Most.
Both mode and most start with the letters MO.
The mode is calculated by examining the data to see which number appears most.
In a testing situation you would likely order the numbers then count the frequency of any
number that appears multiple times to determine the mode.
The mode is the only measure of central tendency you can use for nominal data.
While it can be used for all levels of measurement, it is considered unstable since fluctuations
are likely between sample populations.
Sometimes there is no mode.
If all scores are different the mode does not exist.
Sometimes there are multiple modes.
If several values occur with equal frequency there are several modes.
Unfortunately the mode can't be used for any further calculations in the study -- it can
only help to describe the central tendency of the population.
Take a look at the data from our example.
Which measure of central tendency most accurately represents the data?
Is it the mean, median or mode?
They are all very different.
Comment below with your answer and rationale.
If you aren't sure try watching this video again to pick out your rationale.
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