Difference between revisions of "Central tendency"

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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
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= Concept Map =
 
= Concept Map =
 
__FORCETOC__
 
__FORCETOC__
<mm>[[central_tendency_eng.mm|Flash]]</mm>
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[[File:central_tendency_eng.mm|Flash]]
  
 
= Textbook =
 
= Textbook =
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=Additional Information=
 
=Additional Information=
 
==Useful websites==
 
==Useful websites==
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#This pdf short notes gives simple definitions of mean, median, mode click here [http://www.dentonisd.org/cms/lib/TX21000245/Centricity/Domain/1557/Measures_of_Central_Tendency_notes.pdf/notes]
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#https://en.wikipedia.org/wiki/Arithmetic_mean
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#https://explorable.com/arithmetic-mean
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#http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Arithmetic_mean.html
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==Reference Books==
 
==Reference Books==
  
 
= Teaching Outlines =
 
= Teaching Outlines =
  
==Concept #==
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==Concept #1.MEAN==
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The mean (or average) is the most popular and well known measure of central tendency. It can be used with both discreteand continuous data, although its use is most often with continuous data. 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 x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, then the sample mean, usually denoted by
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[[Image:KOER-%20Mathematics%20-%20Statistics_html_174cec39.gif]]
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(pronounced x bar), is:
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[[Image:KOER-%20Mathematics%20-%20Statistics_html_69b2cf9e.gif]]
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The mean includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.
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===Learning objectives===
 
===Learning objectives===
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#Understand and know that a measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.
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#Understand that the mean, median and mode are all valid measures of central tendency but, under different conditions, some measures of central tendency become more appropriate to use than others.
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# Learn to calculate mean and analyse data and make inferences.
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===Notes for teachers===
 
===Notes for teachers===
===Activity No # ===
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A measure of central tendency is a single value that attempts to describe a set of data by identifying the central
{| style="height:10px; float:right; align:center;"
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position within that set of data. As such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as, the median and the mode.<br> The mean, median and mode are all valid measures of central tendency but, under different conditions, some measures of
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central tendency become more appropriate to use than others.
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
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===Activity===
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
  
===Activity No # ===
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#Activity No #1 [[central tendency mean activity1]]
{| style="height:10px; float:right; align:center;"
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#Activity No #2 [[central tendency mean activity2]]
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
  
==Concept #==
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==Concept #2.MEDIAN==
 
===Learning objectives===
 
===Learning objectives===
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#Understand the median as a measure for central tendency
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#Understand when and when not to use median
 
===Notes for teachers===
 
===Notes for teachers===
===Activity No # ===
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The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less
{| style="height:10px; float:right; align:center;"
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affected by outliers and skewed data.
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===Activity===
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
  
===Activity No # ===
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#Activity No #1 [[central tendency median activity1]]
{| style="height:10px; float:right; align:center;"
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#Activity No #2 [[central tendency median activity2]]
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
  
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==Concept #3.MODE==
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===Learning objectives===
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#Understand the mode as a measure for central tendency
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#Understand when and when not to use mode
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===Notes for teachers===
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The mode is the most frequent score in our data
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set. On a histogram it represents the highest bar in a bar chart or
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histogram. You can, therefore, sometimes consider the mode as being
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the most popular option. An example of a mode is presented below:
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[[Image:KOER-%20Mathematics%20-%20Statistics_html_58d59706.png]]
  
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Normally, the mode is used for categorical data where we wish to know which is the most common category
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===Activity===
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#Activity No #1 [[central tendency mode activity1]]
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#Activity No #2 [[central tendency mode activity2]]
  
 
= Hints for difficult problems =
 
= Hints for difficult problems =
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Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
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[[Category:Central tendency]]

Latest revision as of 10:37, 29 October 2019

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

Textbook

To add textbook links, please follow these instructions to: (Click to create the subpage)

Additional Information

Useful websites

  1. This pdf short notes gives simple definitions of mean, median, mode click here [1]
  2. https://en.wikipedia.org/wiki/Arithmetic_mean
  3. https://explorable.com/arithmetic-mean
  4. http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Arithmetic_mean.html

Reference Books

Teaching Outlines

Concept #1.MEAN

The mean (or average) is the most popular and well known measure of central tendency. It can be used with both discreteand continuous data, although its use is most often with continuous data. 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, then the sample mean, usually denoted by   (pronounced x bar), is:

 

The mean includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.

Learning objectives

  1. Understand and know that a measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.
  2. Understand that the mean, median and mode are all valid measures of central tendency but, under different conditions, some measures of central tendency become more appropriate to use than others.
  3. Learn to calculate mean and analyse data and make inferences.

Notes for teachers

A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as, the median and the mode.
The mean, median and mode are all valid measures of central tendency but, under different conditions, some measures of central tendency become more appropriate to use than others.

Activity

  1. Activity No #1 central tendency mean activity1
  2. Activity No #2 central tendency mean activity2

Concept #2.MEDIAN

Learning objectives

  1. Understand the median as a measure for central tendency
  2. Understand when and when not to use median

Notes for teachers

The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data.

Activity

  1. Activity No #1 central tendency median activity1
  2. Activity No #2 central tendency median activity2

Concept #3.MODE

Learning objectives

  1. Understand the mode as a measure for central tendency
  2. Understand when and when not to use mode

Notes for teachers

The mode is the most frequent score in our data set. On a histogram it represents the highest bar in a bar chart or histogram. You can, therefore, sometimes consider the mode as being the most popular option. An example of a mode is presented below:  

Normally, the mode is used for categorical data where we wish to know which is the most common category

Activity

  1. Activity No #1 central tendency mode activity1
  2. Activity No #2 central tendency mode activity2

Hints for difficult problems

Project Ideas

Math Fun

Usage

Create a new page and type {{subst:Math-Content}} to use this template