Difference between revisions of "Manuals/calci/DEVSQ"
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| − | <div style="font-size:30px">'''DEVSQ( | + | <div style="font-size:30px">'''DEVSQ()'''</div><br/> |
| − | * | + | *Parameters are any set of real numbers. |
| + | **DEVSQ(), returns the sum of squares of deviations. | ||
==Description== | ==Description== | ||
| + | |||
*This function gives the sum of Squares of Deviation of a given set of numbers. | *This function gives the sum of Squares of Deviation of a given set of numbers. | ||
*The steps to calculate: | *The steps to calculate: | ||
| Line 8: | Line 10: | ||
#Find the deviation of each value. For that, subtract all numbers with its mean value. | #Find the deviation of each value. For that, subtract all numbers with its mean value. | ||
#Square each Deviation Values and find its sum. | #Square each Deviation Values and find its sum. | ||
| − | :<math>DEVSQ=\sum( | + | :<math>DEVSQ=\sum(x_i-\bar{x})^2</math> where <math>x_i</math> is the every observation and <math>\bar{x}</math> is the Arithmetic Mean. |
*Here we have to give more than one arguments and arguments can be either numbers,names,logical values, | *Here we have to give more than one arguments and arguments can be either numbers,names,logical values, | ||
arrays or cell references that contain numbers. | arrays or cell references that contain numbers. | ||
*Also cells with the value of '0' are considered and the arguments contains text, logical values or empty cells are ignored. | *Also cells with the value of '0' are considered and the arguments contains text, logical values or empty cells are ignored. | ||
This function will give the result as error, when the text couldn't be converted to numbers. | This function will give the result as error, when the text couldn't be converted to numbers. | ||
| + | |||
| + | ==ZOS== | ||
| + | |||
| + | *The syntax is to calculate DEVSQ in ZOS is <math>DEVSQ()</math>. | ||
| + | **Parameters are any set of real numbers. | ||
| + | *For e.g.,DEVSQ(1.5..7.5..0.3) | ||
| + | {{#ev:youtube|wsr8HO-ByJk|280|center|Average}} | ||
==Examples== | ==Examples== | ||
| Line 20: | Line 29: | ||
#Mean = <math>\frac{50+52+ 54+ 56+ 58+ 60}{6} = \frac{330}{6} = 55</math> | #Mean = <math>\frac{50+52+ 54+ 56+ 58+ 60}{6} = \frac{330}{6} = 55</math> | ||
#Deviation =<math> |50-55|,|52-55|,|54-55|,|56-55|,|58-55|,|60-55| = 5,3,1,1,3,5</math> | #Deviation =<math> |50-55|,|52-55|,|54-55|,|56-55|,|58-55|,|60-55| = 5,3,1,1,3,5</math> | ||
| − | + | #Squares of Deviation = <math>5^2,3^2,1^2,1^2,3^2,5^2 = 25+9+1+1+9+25 = 70</math> | |
*DEVSQ(5,-10,13,-7,9) = 404 | *DEVSQ(5,-10,13,-7,9) = 404 | ||
*DEVSQ(1.2,6.4,8.3,5.7,10) = 44.068 | *DEVSQ(1.2,6.4,8.3,5.7,10) = 44.068 | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|Erd98rj97hI|280|center|Sum of Squared Deviation}} | ||
==See Also== | ==See Also== | ||
| + | |||
*[[Manuals/calci/AVEDEV | AVEDEV]] | *[[Manuals/calci/AVEDEV | AVEDEV]] | ||
*[[Manuals/calci/STDEV | STDEV]] | *[[Manuals/calci/STDEV | STDEV]] | ||
==References== | ==References== | ||
| − | [http://en.wikipedia.org/wiki/Squared_deviations | + | |
| + | [http://en.wikipedia.org/wiki/Squared_deviations Squared Deviations] | ||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 15:55, 7 August 2018
DEVSQ()
- Parameters are any set of real numbers.
- DEVSQ(), returns the sum of squares of deviations.
Description
- This function gives the sum of Squares of Deviation of a given set of numbers.
- The steps to calculate:
- Find the mean.
- Find the deviation of each value. For that, subtract all numbers with its mean value.
- Square each Deviation Values and find its sum.
- where is the every observation and is the Arithmetic Mean.
where 
is the every observation and 
is the Arithmetic Mean.- Here we have to give more than one arguments and arguments can be either numbers,names,logical values,
arrays or cell references that contain numbers.
- Also cells with the value of '0' are considered and the arguments contains text, logical values or empty cells are ignored.
This function will give the result as error, when the text couldn't be converted to numbers.
ZOS
- The syntax is to calculate DEVSQ in ZOS is .
- Parameters are any set of real numbers.
- For e.g.,DEVSQ(1.5..7.5..0.3)
.
Examples
- DEVSQ(50,52, 54, 56, 58, 60)
Steps
- Mean =
- Deviation =
- Squares of Deviation =
- DEVSQ(5,-10,13,-7,9) = 404
- DEVSQ(1.2,6.4,8.3,5.7,10) = 44.068
Related Videos
See Also
References