HSC Commerce (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Obtain the trend values for the data, using 3-yearly moving averages

Use the method of least squares to fit a trend line to the data given below. Also, obtain the trend value for the year 1975.

The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.

1. Obtain trend values for the above data using 5-yearly moving averages.
2. Plot the original time series and trend values obtained above on the same graph.

Following table shows the all India infant mortality rates (per ‘000) for years 1980 to 2010

Fit a trend line by the method of least squares

Solution: Let us fit equation of trend line for above data.

Let the equation of trend line be y = a + bx   .....(i)

Here n = 7(odd), middle year is `square` and h = 5

The normal equations are

Σy = na + bΣx

As, Σx = 0, a = `square`

Also, Σxy = aΣx + bΣx²

As, Σx = 0, b =`square`

∴ The equation of trend line is y = `square`

Obtain trend values for data, using 3-yearly moving averages
Solution:

Fit equation of trend line for the data given below.

Let the equation of trend line be y = a + bx   .....(i)

Here n = `square` (even), two middle years are `square` and 2011, and h = `square`

The normal equations are Σy = na + bΣx

As Σx = 0, a = `square`

Also, Σxy = aΣx + bΣx²

As Σx = 0, b = `square`

Substitute values of a and b in equation (i) the equation of trend line is `square`

To find trend value for the year 2016, put x = `square` in the above equation.

y = `square`

Complete the table using 4 yearly moving average method.

Choose the correct alternative:

The Cost of Living Index Number using Weighted Relative Method is given by

State whether the following statement is True or False:

For Cost of Living Index Number CLI =`(sum"IW")/(sum"W")`, where I = `("P"_0)/("P"_1) xx 100` and w = p₀q₀

Calculate the Cost of Living Index by Family Budget method in following example where W are wages of base year and I are current year price relatives.

Find the missing wage if the Cost of Living Index for the following data is 150.

Choose the correct alternative:

The optimal sequence for above data is

Choose the correct alternative:

If there are 3 machines A, B and C, conditions for reducing a 3 machine problem to a 2 machine problem with respect to minimum processing time is ______

If there are n jobs and m machines, then there will be _______ sequence of doing jobs.

Choose the correct alternative:

In solving 2 machine and n jobs sequencing problem, the following assumption is wrong

In assignment problem each worker or machine is ______ capable of handling any job

______ time is the time when the machine is available but is waiting for a job to be processed

In sequencing problem the time required to transfer a job from one machine to another is ______

State whether the following statement is True or False: 

One of the assumptions is made while sequencing n jobs on 2 machines is: two jobs must be loaded at a time on any machine

State whether the following statement is True or False:

The Total Elapsed is the time required to complete all the jobs i.e. entire task