Measures of Central Tendency

What is a measure of central tendency?

A measure of central tendency is a single value that is used to describe an entire population or group of data. This value is usually the central value in which the other data points cluster around. A real life example of this is a stereotype because a stereotype is a representation of a certain kind of person, ie. an emo or jock.

Why use measures of central tendency?

We use measures of central tendency because we cannot use every single data value to represent the data set. There’d be too many to count. Therefore, we have to use a single value to represent all of them. This can be compared to a president or prime minister. The president or prime minster represent their entire country because every single person in the country could not go to a nato or un conference.


Mean/Average:

What is the mean?

  • The population mean is represented by μ.
  • µ=(∑x)/n
  • The sample mean is represented x̄.
  • x̄ = (∑x)/n

  • Where x is all of the data values in a data set
  • and n is sample size

Example:

You have taken a sample of  the amount of girlfriends every boy has had in your class. You want to find the mean. The sample is respectively 0,1,5,2,0,10.

Screen Shot 2017-07-08 at 12.04.39 AM.png


Mode:

What is the mode?

  • The mode is the number that occurs the most often.

Example:

You are taking a sample of how many fish polar bears eat in an hour. You count that 5 polar bears ate 40 fish, 30 polar bears ate 50 fish, and 10 polar bears ate 60 fish.

50 is the mode because the most amount of polar bears ate 50 fish.


Median:

What is the median?

  • The median is the value lying in the middle.
  • It is found by putting all of the data in numerical order and then counting one off each side until you reach the middle.

Example:

You have taken a sample of the number of trees at schools across the United States. The data is respectively 20, 4, 39, 13, 23, 40, 10, 389, and 3.

Screen Shot 2017-07-08 at 12.15.23 AM.png

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