Dustin K MacDonald

Menu
  • Home
  • About
  • Economic and Community Development
  • Nonprofit Management
    • Counselling and Service Delivery
    • Suicide Prevention / Crisis Intervention
  • Politics and Governance
  • Math and Statistics
  • Salesforce
Menu

Measures of Central Tendency

Posted on January 24, 2015November 25, 2018 by Dustin

The measures of central tendency are processes for determining what the central value in a dataset is. The most common is the arithmetic average, or mean – so this value has come to be known as simply the average.

The three measures of central tendency are mean, median and mode.

Table of Contents

Mean

To calculate the mean (also known as the arithmetic mean or arithmetic average), you take all of the scores, add up  their values and divide them by the number you have. Let’s look at the following values of student values out of 10:

4 4 4 5 5 5 6 6
6 6 6 6 6 7 7 7
7 7 7 7 7 7 7 7
7 8 8 8 8 8 8 8
8 8 9 9 9 9 9 10

 

There are 40 values here. If we add them all up, we get the total 280. Dividing by the number of values, we get an average of:

  • / 40 = 7

Median

The mean is a very common distribution but can be affected by extreme sources. If any values are very high or very low compared to the majority, the mean can be affected. In situations like this, we use the median. The median is the middle value in the set of scores.

For instance, let’s look at a limited set of numbers from the above data set:

4 4 4 5 5 5 6

There are 7 values here, so the middle value, 5 becomes the median. In a situation like our full chart above where we have 40 values, we instead have two middle values.

17 18 19 20 21 22 23 24
7 7 7 7 7 7 7 7

 

Taking values 20 and 21 (7 + 7) and dividing them by 2 gives us the median 7.

Mode

Finally, the mode is simply the most common score occurring in a distribution. In the full data set above, we have the following values and frequencies:

Value Frequency
4 3
5 3
6 7
7 12
8 9
9 5
10 2

 

In this case, 7 appears twelve times, so it becomes our median.

Choosing a Measure of Central Tendency

The mean is most commonly used – it is the best for symmetric distributions (distributions without major outliers.) The median is best for a skewed distribution or one with outlier(s), while the mode is used in 3 cases:

  • One particular score dominates a distribution
  • Distribution is bimodal or multimodal
  • Data are nominal

Weighted Mean

One special case of the mean is the “weighted mean”, where some values are “weighted” or contribute more to the total value than others. The data set from above is presented here:

Value Frequency
4 3
5 3
6 7
7 12
8 9
9 5
10 2

 

To calculate the weighted mean, we multiply each value by its frequency, before dividing by the frequency. This is similar to the mean as you’ll see:

  • 3×4 + 3×5 + 7×6 + 12×7 + 9×8 + 5×9 + 10×2
    = 12 + 15 + 42 + 84 + 72 + 45 + 20
    = 290
  • We divide by the original frequencies:

3 + 3 + 7 + 12 + 9 + 5 + 2
= 41

  • And now we’ll divide the top by the bottom:290 / 41 = 7.073



Cite this article as: MacDonald, D.K., (2015), "Measures of Central Tendency," retrieved on October 2, 2023 from https://dustinkmacdonald.com/measures-of-central-tendency/.

3 thoughts on “Measures of Central Tendency”

  1. Pingback: An Introduction to Intelligence Analysis and Research | Dustin K. MacDonaldDustin K. MacDonald
  2. Pingback: An Introduction to Intelligence Research and Analysis - Intelligence Analyst Training
  3. Pingback: Scales of Measurement - Dustin K MacDonald

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Privacy Policy

See here for our privacy policy. This site uses affiliate links and Adsense ads to provide targeted advertising.

Tags

analytical technique assessment city council communication community development counselling crisis chat crisis intervention data science eastern university economic development education empathy evaluation forecasting fundraising governance humint intelligence intelligence analysis keokuk county language learning legal local government management peer support personal development politics professional development protective factors psychosocial risk factors safety planning salesforce sigourney social media statistics suicide suicide assessment suicide risk assessment technology terrorism training violence risk assessment youth

Recommended Posts

  • Conducting Psychosocial Assessments
  • DCIB Model of Suicide Risk Assessment
  • ABC Model of Crisis Intervention
  • My Friend is Suicidal - What do I do?

Recent Posts

  • ITS834 Emerging Threats and Countermeasures
  • Salesforce Flow that autonames records
  • Salesforce formula that calculates age
  • Earning the Project Management Professional (PMP)
  • ITS831 Information Technology Importance in Strategic Planning

Archives

  • September 2023 (3)
  • August 2023 (1)
  • July 2023 (1)
  • May 2023 (1)
  • March 2023 (1)
  • February 2023 (2)
  • January 2023 (4)
  • December 2022 (2)
  • May 2022 (1)
  • April 2022 (2)
  • March 2022 (1)
  • February 2022 (1)
  • December 2021 (1)
  • October 2021 (1)
  • August 2021 (2)
  • May 2021 (3)
  • December 2020 (1)
  • November 2020 (4)
  • July 2020 (1)
  • June 2020 (1)
  • April 2020 (1)
  • March 2020 (4)
  • February 2020 (7)
  • January 2020 (1)
  • November 2019 (1)
  • October 2019 (2)
  • September 2019 (4)
  • August 2019 (2)
  • March 2019 (1)
  • February 2019 (1)
  • January 2019 (1)
  • December 2018 (4)
  • November 2018 (3)
  • October 2018 (3)
  • September 2018 (19)
  • October 2017 (2)
  • September 2017 (2)
  • August 2017 (1)
  • July 2017 (39)
  • May 2017 (3)
  • April 2017 (4)
  • March 2017 (4)
  • February 2017 (4)
  • January 2017 (5)
  • December 2016 (4)
  • November 2016 (4)
  • October 2016 (5)
  • September 2016 (4)
  • August 2016 (5)
  • July 2016 (5)
  • June 2016 (5)
  • May 2016 (3)
  • April 2016 (2)
  • March 2016 (2)
  • February 2016 (2)
  • January 2016 (4)
  • December 2015 (2)
  • November 2015 (2)
  • October 2015 (2)
  • September 2015 (2)
  • August 2015 (1)
  • June 2015 (2)
  • May 2015 (5)
  • April 2015 (3)
  • March 2015 (8)
  • February 2015 (12)
  • January 2015 (28)

Meta

  • Log in
  • Entries feed
  • Comments feed
  • WordPress.org

Recent Comments

  • ITS834 Emerging Threats and Countermeasures. - Dustin K MacDonald on University of the Cumberlands PhD in Information Technology
  • Earning the Project Management Professional (PMP) - Dustin K MacDonald on University of the Cumberlands PhD in Information Technology
  • Dustin on How I Got a Book Contract
  • Ananth on How I Got a Book Contract
  • Aly on Improving Your Helpline Work

Tags

analytical technique assessment city council communication community development counselling crisis chat crisis intervention data science eastern university economic development education empathy evaluation forecasting fundraising governance humint intelligence intelligence analysis keokuk county language learning legal local government management peer support personal development politics professional development protective factors psychosocial risk factors safety planning salesforce sigourney social media statistics suicide suicide assessment suicide risk assessment technology terrorism training violence risk assessment youth
© 2023 Dustin K MacDonald | Powered by Minimalist Blog WordPress Theme