MARKED

CENTRAL TENDANCY
Central Tendancy refers to a typical value of data, or the "middle" value. This is measured using mean, median and mode.
definitions
  • mean: sometimes called the "average", found by calculating the sum of the data, and dividing that by the number of numbers.
  • Median: the middle value when a set of date is arranged in numarical order. if there is an even number of data, the median is the average of the middle two numbers.
  • Mode: the number that occurs most often in a set of data. There may be more than one mode.
  • Range: the differnce between the greatest and lowest values in a set of data.

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The mean is the average of a set of numbers. To find the mean, you add up all the numbers in a set of data, then divide that answer by the number of data values. For instance, say you had the number values of: 3,4,6,8,11,12,6,5,8 and 4. You would add these numbers up to get 133. Then you would divide by the number of values which is 10. So, 133/10 = 13.3. And so, the mean of these number values is 13.3.



  • For three numbers, add them and divide them by 3:
frac{x_1 + x_2 + x_3}{3}.
frac{x_1 + x_2 + x_3}{3}.

  • For four numbers, add them and divide by 4:
frac{x_1 + x_2 + x_3 + x_4}{4}.
frac{x_1 + x_2 + x_3 + x_4}{4}.



MEDIAN
The median is the middle number in a set of numbers.
To find the median you must aranange the numbers in numerical order.
If there are two medians you must average them.

Example
The set of numbers given is 5, 16, 3, 20, 32, 4, 15, 23
  1. Put the numbers in numerical order. (3,4,5,15,16,20,23,32)
  2. Then find the middle number or numbers. (3,4,5,15,16,20,23,32)
  3. There Are two numbers so average them! (15+16\2) = (31\2) = 15.5
4. End the question with a therefore statement (Therefore the Median is 15.5)


MODE
The mode is the number in a set of data that comes up the most, also the most frequent measure. To find the mode you just count up and find the number that occurs the most, there can be more then one number that occurs, this is called multi-modal.

Example
Find the mode of 5,12,7,6,10,11,7,1,7
You would then look to find the number that occurs the most, in this example 7 occurs the most,
mode-7

Find the mode of 11,5,7,9,11,9,2,11,9
In this example there are two numbers that occur the most.
mode-11,9



RANGE
The range is the difference between the highest and lowest values in a set of data. To find the range you take the lowest number and subtract it from the highest number.

Example
Find the range of 5,6,7,8,23,15,11
You would then take the higest number and lowest and subtract them.
23-5=18


Knill, G (1999). Mathpower 9. Toronto, Ontario: Mcgraw-Hill Ryerson.
(2008). Wikipedia. Retrieved December 18, 2008, from Mode (statistics) Web site: http://en.wikipedia.org/wiki/Mode_(statistics)
(2008). Wikipedia. Retrieved December 18, 2008, from Mean (statistics) Web site: http://en.wikipedia.org/wiki/Mean_(statistics)