Manuals/calci/DEVSQ

DEVSQ(n1,n2...)

• $n_{1},n_{2}..$ are any real numbers.

Description

• This function gives the sum of Squares of Deviation of a given set of numbers.
• The steps to calculate:

1. Find the mean.
2. Find the deviation of each value. For that, subtract all numbers with its mean value.
3. Square each Deviation Values and find its sum.

$DEVSQ=\sum (x_{i}-{\bar {x}})^{2}$ where $x_{i}$ is the every observation and ${\bar {x}}$ 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 Section

• The syntax is to calculate DEVSQ in ZOS is $DEVSQ(n_{1},n_{2},....)$.
  • where $n_{1},n_{2}..$ are any real numbers.
• For e.g.,DEVSQ(1.5..7.5..0.3)

Average

Examples

• DEVSQ(50,52, 54, 56, 58, 60)

Steps

1. Mean = ${\frac {50+52+54+56+58+60}{6}}={\frac {330}{6}}=55$
2. Deviation =$|50-55|,|52-55|,|54-55|,|56-55|,|58-55|,|60-55|=5,3,1,1,3,5$
3. Squares of Deviation = $5^{2},3^{2},1^{2},1^{2},3^{2},5^{2}=25+9+1+1+9+25=70$

• DEVSQ(5,-10,13,-7,9) = 404
• DEVSQ(1.2,6.4,8.3,5.7,10) = 44.068

See Also

• AVEDEV
• STDEV

References

Squared Deviations