BIOLOGY FOR LIFE
  • Syllabus
    • Core >
      • 1: Cell Biology >
        • 1.1: Introduction to Cells
        • 1.2: Ultrastructure of Cells
        • 1.3: Membrane Structure
        • 1.4: Membrane Transport
        • 1.5: The Origin of Cells
        • 1.6: Cell Division
      • 2: Molecular Biology >
        • 2.1: Molecules to Metabolism
        • 2.2: Water
        • 2.3: Carbohydrates and Lipids
        • 2.4: Proteins
        • 2.5: Enzymes
        • 2.6: DNA and RNA
        • 2.7: DNA Replication, Transcription and Translation
        • 2.8: Cell Respiration
        • 2.9: Photosynthesis
      • 3: Genetics >
        • 3.1: Genes
        • 3.2: Chromosomes
        • 3.3: Meiosis
        • 3.4: Inheritance
        • 3.5: Genetic Modification and Biotechnology
      • 4: Ecology >
        • 4.1: Species, Communities and Ecosystems
        • 4.2: Energy Flow
        • 4.3: Carbon Cycling
        • 4.4: Climate Change
      • 5: Evolution and Biodiversity >
        • 5.1: Evidence for Evolution
        • 5.2: Natural Selection
        • 5.3: Classification and Biodiversity
        • 5.4: Cladistics
      • 6: Human Physiology >
        • 6.1: Digestion and Absorption
        • 6.2: The Blood System
        • 6.3: Defense Against Infectious Disease
        • 6.4: Gas Exchange
        • 6.5: Neurons and Synapses
        • 6.6: Hormones, Homeostasis and Reproduction
    • Higher Level >
      • 7: Nucleic Acids >
        • 7.1: DNA Structure and Replication
        • 7.2: Transcription and Gene Expression
        • 7.3: Translation
      • 8: Metabolism, Cell Respiration & Photosynthesis >
        • 8.1: Metabolism
        • 8.2: Cell Respiration
        • 8.3: Photosynthesis
      • 9: Plant Biology >
        • 9.1: Transport in the Xylem of Plants
        • 9.2: Transport in the Phloem of Plants
        • 9.3: Growth in Plants
        • 9.4: Reproduction in Plants
      • 10: Genetics and Evolution >
        • 10.1: Meiosis
        • 10.2: Inheritance
        • 10.3: Gene Pools and Speciation
      • 11: Animal Physiology >
        • 11.1: Antibody Production and Vaccination
        • 11.2: Movement
        • 11.3: Kidney and Osmoregulation
        • 11.4: Sexual Reproduction
    • Options >
      • D: Human Physiology >
        • D.1: Human Nutrition
        • D.2: Digestion
        • D.3: Functions of the Liver
        • D.4: The Heart
        • D.5: Hormones and Metabolism
        • D.6: Transport of Respiratory Gases
  • IB Requirements
    • Learner Profile
    • Group 4 Project
    • External Exam
    • Internal Assessment >
      • Personal Engagement
      • Exploration
      • Analysis
      • Evaluation
      • Communication
    • Extended Essay
  • Investigation Skills
    • Lab Safety
    • Microscopy
    • Lab Drawings
    • Data Tables
    • Measurement
    • Statistics >
      • Descriptive Statistics >
        • Skew
        • Measures of Central Tendancy
        • Measures of Spread
        • Pearson Correlation
      • Inferential Statistics >
        • T-Test
        • ANOVA
        • Kruskal-Wallis
        • X2 Test for Independence
        • X2 Goodness of Fit
    • Graphing >
      • Graphing with Excel
      • Interpreting Error Bars
    • Error Analysis
  • Course Info
    • Above & Beyond >
      • Biology Club
      • Pumpkin Carving
      • Scavenger Hunt
      • Science News
      • IB Bio Dance
      • Wood Duck Project
      • Invasive Crayfish Project
    • Assessment >
      • Class Grading IB Bio I
      • Class Grading IB Bio II
      • Daily Quizzes
      • Lab Practicals
    • Class Photos
    • Recommendations
    • Supplemental Reading
  • Contact
  • About
    • Philosophy
    • Resume
    • Reflection
    • Site Feedback
    • Favorite Quotes
    • AEF Blog
  • Expeditions
    • Bahamas (2009)
    • Trinidad (2010)
    • Trinidad (2011)
    • Ecuador (2012)
    • Trinidad (2013)
    • Peru (2014)
    • Bahamas (2015)
    • Peru (2016)
    • Costa Rica (2017)
    • Costa Rica (2018)
    • Arizona (2022)
    • Florida (2023)
  • Summer Ecology Research

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)
​
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:
Picture

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)
​

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)
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"When we try to pick out anything by itself, we find it hitched to everything else in the Universe." 
 John Muir,   1911
  • Syllabus
    • Core >
      • 1: Cell Biology >
        • 1.1: Introduction to Cells
        • 1.2: Ultrastructure of Cells
        • 1.3: Membrane Structure
        • 1.4: Membrane Transport
        • 1.5: The Origin of Cells
        • 1.6: Cell Division
      • 2: Molecular Biology >
        • 2.1: Molecules to Metabolism
        • 2.2: Water
        • 2.3: Carbohydrates and Lipids
        • 2.4: Proteins
        • 2.5: Enzymes
        • 2.6: DNA and RNA
        • 2.7: DNA Replication, Transcription and Translation
        • 2.8: Cell Respiration
        • 2.9: Photosynthesis
      • 3: Genetics >
        • 3.1: Genes
        • 3.2: Chromosomes
        • 3.3: Meiosis
        • 3.4: Inheritance
        • 3.5: Genetic Modification and Biotechnology
      • 4: Ecology >
        • 4.1: Species, Communities and Ecosystems
        • 4.2: Energy Flow
        • 4.3: Carbon Cycling
        • 4.4: Climate Change
      • 5: Evolution and Biodiversity >
        • 5.1: Evidence for Evolution
        • 5.2: Natural Selection
        • 5.3: Classification and Biodiversity
        • 5.4: Cladistics
      • 6: Human Physiology >
        • 6.1: Digestion and Absorption
        • 6.2: The Blood System
        • 6.3: Defense Against Infectious Disease
        • 6.4: Gas Exchange
        • 6.5: Neurons and Synapses
        • 6.6: Hormones, Homeostasis and Reproduction
    • Higher Level >
      • 7: Nucleic Acids >
        • 7.1: DNA Structure and Replication
        • 7.2: Transcription and Gene Expression
        • 7.3: Translation
      • 8: Metabolism, Cell Respiration & Photosynthesis >
        • 8.1: Metabolism
        • 8.2: Cell Respiration
        • 8.3: Photosynthesis
      • 9: Plant Biology >
        • 9.1: Transport in the Xylem of Plants
        • 9.2: Transport in the Phloem of Plants
        • 9.3: Growth in Plants
        • 9.4: Reproduction in Plants
      • 10: Genetics and Evolution >
        • 10.1: Meiosis
        • 10.2: Inheritance
        • 10.3: Gene Pools and Speciation
      • 11: Animal Physiology >
        • 11.1: Antibody Production and Vaccination
        • 11.2: Movement
        • 11.3: Kidney and Osmoregulation
        • 11.4: Sexual Reproduction
    • Options >
      • D: Human Physiology >
        • D.1: Human Nutrition
        • D.2: Digestion
        • D.3: Functions of the Liver
        • D.4: The Heart
        • D.5: Hormones and Metabolism
        • D.6: Transport of Respiratory Gases
  • IB Requirements
    • Learner Profile
    • Group 4 Project
    • External Exam
    • Internal Assessment >
      • Personal Engagement
      • Exploration
      • Analysis
      • Evaluation
      • Communication
    • Extended Essay
  • Investigation Skills
    • Lab Safety
    • Microscopy
    • Lab Drawings
    • Data Tables
    • Measurement
    • Statistics >
      • Descriptive Statistics >
        • Skew
        • Measures of Central Tendancy
        • Measures of Spread
        • Pearson Correlation
      • Inferential Statistics >
        • T-Test
        • ANOVA
        • Kruskal-Wallis
        • X2 Test for Independence
        • X2 Goodness of Fit
    • Graphing >
      • Graphing with Excel
      • Interpreting Error Bars
    • Error Analysis
  • Course Info
    • Above & Beyond >
      • Biology Club
      • Pumpkin Carving
      • Scavenger Hunt
      • Science News
      • IB Bio Dance
      • Wood Duck Project
      • Invasive Crayfish Project
    • Assessment >
      • Class Grading IB Bio I
      • Class Grading IB Bio II
      • Daily Quizzes
      • Lab Practicals
    • Class Photos
    • Recommendations
    • Supplemental Reading
  • Contact
  • About
    • Philosophy
    • Resume
    • Reflection
    • Site Feedback
    • Favorite Quotes
    • AEF Blog
  • Expeditions
    • Bahamas (2009)
    • Trinidad (2010)
    • Trinidad (2011)
    • Ecuador (2012)
    • Trinidad (2013)
    • Peru (2014)
    • Bahamas (2015)
    • Peru (2016)
    • Costa Rica (2017)
    • Costa Rica (2018)
    • Arizona (2022)
    • Florida (2023)
  • Summer Ecology Research