Measures of Central Tendancy

Measures of Central Tendency are ways of describing the central position of a frequency distribution for a group of data.  You can describe this central position using the mean, median, or mode.  Which you use will depend on how much and the type of data you collected.

​Type of Data for Responding Variable	​Best Measure of Central Tendency
Qualitative Nominal (no ranking or order)	Mode
​Qualitative Ordinal (has ranking or order)	Median
​Quantitative  With majority of skew values less than |1.0|	Mean
​Quantitative With majority of skew values more than |1.0|	Median

Mean

The arithmetic mean is the most commonly used measure of central tendency.  The mean is essentially a model of a data set for normally distributed (non-skewed) data.   The mean has one main disadvantage: it is particularly susceptible to the influence of outliers. These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. That’s why we determined the skew.

• DO NOT calculate a mean for skewed data. 
• ​DO NOT calculate a mean from values that are already averages. 
• DO NOT calculate a mean when the measurement scale is not linear (i.e. pH units are not measured on a linear scale)

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The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. So, if we have N values in a data set and they have values x1,x2, … ,xn, the sample mean, usually denoted by x̄ (pronounced "x bar"), is:

Calculating the Mean in Sheets

• ​​In our class, the formula we'll want to  use is  =AVERAGE(A1:A100).  Replace A1:A100 with your data by highlighting the cells with data you want to include in the mean calculation.
• Calculating the Mean in Google Sheets (website)
• Finding the Mean in Google Sheets (video)
• Changing the number of digits displayed in your Google Sheet (website)

Calculating the Mean in Excel

Open Excel and enter your data in columns.  You can label the columns if you prefer.  To calculate mean:

• Click on the box in which you want the mean to be placed  
• Click the "Formulas" tab at the top of the screen
• Select the “Insert Function button”
• ​A new box pops up.  Search to find the AVERAGE option, click OK  ​
• Highlight the data of which you want the average to be calculated, click OK
• Be sure your mean has the correct number of digits. Your processed data should have the same number of digits as your raw data.  To do this, click the box which is displaying the mean and on the "Home" tab click the decrease decimal button until you have the correct number of digits showing.

Median

The median is the middle score for a set of data that has been arranged in order of magnitude. The median should be used if there are outliers or skewed data (meaning the data does not fit a “normal distribution”). 

• Online calculators, such as ttps://www.calculatorsoup.com/calculators/statistics/mean-median-mode.php 
  
• ​Excel or Google Sheets =MEDIAN(highlight data cells)

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Mode

The mode is the most frequent score in a data set.  Calculate the mode by tallying the result that is repeated more often than any other.

• Online calculators, such as ttps://www.calculatorsoup.com/calculators/statistics/mean-median-mode.php 
• Excel or Google Sheets =MODE(highlight data cells)