Applied Statistics Important Formulas

Dear students, before you start revision for the chapter Applied Statistics, first make sure you revise all the formulas and key points. Only if you are thorough with the main concepts and formulas, you can confidently work out all the sums. That said, here are the most important formulas in Lesson 9 Applied Statistics, Class 12 Business Maths.

Applied Statistics Important Formulas

Method of Least Squares

$a=\dfrac{\Sigma Y}{n}=\bar {Y}\\$
$b=\dfrac{\Sigma XY}{\Sigma X^{2}}\\$
$\text{The straight line equation: Y = a + bX}\\$
$\text{Two Normal Equations are:} \\$
$\Sigma Y = n a + b \Sigma X \\$
$\Sigma XY = a \Sigma X + b \Sigma X^{2} \\$

Methods of Measuring Seasonal Variations

Method of Simple Averages:

$\text{Seasonal Index (S.I) =}\dfrac{\text{Seasonal Average}}{\text{Grand average}}\times 100\\$

If the data is given in months:

$\text{Seasonal Index (S.I) =}\dfrac{\text{Monthly Average}}{\text{Grand average}}\times 100\\$

If the data is given in quarter:

$\text{Seasonal Index (\text{S.I for Kth Quarter }) =}\dfrac{\text{Average of Kth Quarter}}{\text{Grand average}}\times 100\\$

Weighted Index Number

$\text{Price Index }(P_{01})=\dfrac{\Sigma p_{1}(w)}{p_{0}(w)}\times 100 \\$
$\text{Laspeyre's price index number}=\dfrac{\Sigma p_{1}q_{0} }{p_{0}q_{0}}\times 100 \\$
$\text{Paasche's price index number}=\dfrac{\Sigma p_{1}q_{1} }{p_{0}q_{1}}\times 100 \\$
$\text{Fisher's price index number}=\sqrt{\dfrac{\Sigma p_{1}q_{0}\times\Sigma p_{1}q_{1} }{p_{0}q_{0}\times \Sigma p_{0}q_{1}}} \times 100 \\$
$\text{where}\; p_{0}= \text{base year price; }\\$
$\text{where}\; p_{1}= \text{current year price; }\\$
$\text{where}\; q_{0}= \text{base year quantity; }\\$
$\text{where}\; q_{1}= \text{base year quantity; }\\$

$\text{Time Reversal Test} : P_{01} \times P_{10} = 1\\$
$\text{Factor Reversal Test:} P_{01} \times Q_{01}=\dfrac{\Sigma p_{1}q_{1}}{\Sigma p_{0}q_{0}}\\$

Cost of Living Index Number

$\text{Aggregate Expenditure Method}=\dfrac{\Sigma p_{1}q_{0}}{\Sigma p_{0}q_{0}}\times 100\\$
$\text{Family Budget Method}=\dfrac{\Sigma PV}{\Sigma V}\\$

Control Charts

$\text{(i) Centre Line (CL) indicates the desired standard level of the process.}\\$
$\text{(ii) Upper Control Limit (UCL) indicates the upper limit of tolerance.}\\$
$\text{(iii) Lower Control Limit (LCL) indicates the lower limit of tolerance.}\\$

Control Limits for Mean Chart

$\text{When }\bar {X} \text{and SD are given}\\$

$UCL=\bar {\bar X}+3\frac{\sigma}{\sqrt{n}}\\$

$CL=\bar {\bar X} \\$

$LCL=\bar {\bar X}-3\frac{\sigma}{\sqrt{n}} \\$

$\text{When }\bar {X} \text{and SD are not given}\\$

$UCL=\bar {\bar X}+A_{2}\bar {R}\\$
$CL=\bar {\bar X} \\$
$LCL=\bar {\bar X}-A_{2}\bar {R}\\$

Control Limits for Range Chart

$\text{When SD is given}\\$

$UCL=\bar { R}+3\sigma_{R}\\$
$CL=\bar { R}\\$
$LCL=\bar { R}-3\sigma_{R}\\$

$\text{When SD is not given}\\$

$UCL=D_{4}\bar { R}\\$
$CL=\bar { R}\\$
$LCL=D_{3}\bar { R}\\$

$\bar {X}=\dfrac{\Sigma X}{n}\\$
$\bar {\bar X}=\dfrac{\Sigma \bar X}{\text{No. of sample means}}\\$
$R=X_{max}-X_{min}\\$
$\bar {R}=\dfrac{\Sigma R}{n}\\$

Now that you have revised the important formulas, here are the links to the text book exercise solutions.

Applied Statistics Important Formula

Solutions to Applied Statistics Exercise 9.1

Solutions to Applied Statistics Exercise 9.2

Solutions to Applied Statistics Exercise 9.3

Solutions to Applied Statistics Exercise 9.4

Applied Statistics Important Formulas