Samacheer Kalvi solutions for Business Mathematics and Statistics [English] Class 12 TN Board chapter 9 - Applied Statistics [Latest edition]

Define Time series

What is the need for studying time series?

State the uses of time series

Mention the components of the time series

Define secular trend

Write a brief note on seasonal variations

Explain cyclic variations

Discuss about irregular variation

Define seasonal index

Explain the method of fitting a straight line

State the two normal equations used in fitting a straight line

State the different methods of measuring trend

Compute the average seasonal movement for the following series

The following figures relates to the profits of a commercial concern for 8 years

Find the trend of profits by the method of three yearly moving averages

Find the trend of production by the method of a five-yearly period of moving average for the following data:

The following table gives the number of small-scale units registered with the Directorate of Industries between 1985 and 1991. Show the growth on a trend line by the free hand method.

The annual production of a commodity is given as follows:

Fit a straight line trend by the method of least squares

Determine the equation of a straight line which best fits the following data 

Compute the trend values for all years from 2000 to 2004

The sales of a commodity in tones varied from January 2010 to December 2010 as follows:

Fit a trend line by the method of semi-average

Use the method of monthly averages to find the monthly indices for the following data of production of a commodity for the years 2002, 2003 and 2004

Calculate the seasonal indices from the following data using the average method:

The following table shows the number of salesmen working for a certain concern:

Use the method of least squares to fit a straight line and estimate the number of salesmen in 1997

Define Index Number

State the uses of Index Number

Mention the classification of Index Number

Define Laspeyre’s price index number

Explain Paasche’s price index number

Write note on Fisher’s price index number

State the test of adequacy of index number

Define Time Reversal Test

Explain factor reversal test

Define true value ratio

Discuss about Cost of Living Index Number

Define family budget method

State the uses of cost of Living Index Number

Calculate by a suitable method, the index number of price from the following data:

Calculate price index number for 2005 by (a) Laspeyre’s (b) Paasche’s method

Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s Index numbers for the 2010 from the following data.

Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?

Using Fisher’s Ideal Formula, compute price index number for 1999 with 1996 as base year, given the following:

Calculate Fisher’s index number to the following data. Also show that it satisfies Time Reversal Test.

The following are the group index numbers and the group weights of an average working class family’s budget. Construct the cost of living index number:

Construct the cost of living Index number for 2015 on the basis of 2012 from the following data using family budget method.

Calculate the cost of living index by aggregate expenditure method:

Define Statistical Quality Control

Mention the types of causes for variation in a production process

Define chance cause

Define assignable cause

What do you mean by product control?

What do you mean by process control?

Define a control chart

Name the control charts for variables

Define the mean chart

Define R chart

What are the uses of statistical quality control?

Write the control limits for the mean chart

Write the control limits for the R chart

A machine is set to deliver packets of a given weight. Ten samples of size five each were recorded. Below are given relevant data:

Calculate the control limits for mean chart and the range chart and then comment on the state of control, (conversion factors for n = 5, A₂ = 0.58, D₃ = 0 and D₄ = 2.115)

Ten samples each of size five are drawn at regular intervals from a manufacturing process. The sample means `(bar"X")` and their ranges (R) are given below:

Calculate the control limits in respect of `bar"X"` chart. (Given A₂ = 0.58, D₃ = 0 and D₄ = 2.115) Comment on the state of control

Construct `bar"X"` and R charts for the following data:

(Given for n = 3, A₂ = 1.023, D₃ = 0 and D₄ = 2.574)

The following data show the values of sample mean `(bar"X")` and its range (R) for the samples of size five each. Calculate the values for control limits for mean, range chart and determine whether the process is in control.

(conversion factors for n = 5, A₂ = 0.58, D₃ = 0 and D₄ = 2.115)

A quality control inspector has taken ten ” samples of size four packets each from a potato chips company. The contents of the sample are given below, Calculate the control limits for mean and range chart.

(Given for n = 5, A₂ = 0.58, D₃ = 0 and D₄ = 2.115)

The following data show the values of sample means and the ranges for ten samples of size 4 each. Construct the control chart for mean and range chart and determine whether the process is in control.

In a production process, eight samples of size 4 are collected and their means and ranges are given below. Construct mean chart and range chart with control limits.

In a certain bottling industry the quality control inspector recorded the weight of each of the 5 bottles selected at random during each hour of four hours in the morning.

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A time series is a set of data recorded

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A time series consists of

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The components of a time series which is attached to short term fluctuation is

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Factors responsible for seasonal variations are

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The additive model of the time series with the components T, S, C and I is

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Least square method of fitting a trend is

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The value of ‘b’ in the trend line y = a + bx is

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The component of a time series attached to long term variation is trended as

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The seasonal variation means the variations occurring with in

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Another name of consumer’s price index number is:

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Cost of living at two different cities can be compared with the help of

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Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

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Most commonly used index number is:

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Consumer price index are obtained by:

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Which of the following Index number satisfy the time reversal test?

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While computing a weighted index, the current period quantities are used in the:

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The quantities that can be numerically measured can be plotted on a

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How many causes of variation will affect the quality of a product?

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Variations due to natural disorder is known as

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The assignable causes can occur due to

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A typical control charts consists of

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`bar"X"` chart is a

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R is calculated using

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The upper control limit for `bar"X"` chart is given by

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The LCL for R chart is given by

Using three yearly moving averages, Determine the trend values from the following data.

From the following data, calculate the trend values using fourly moving averages.

Fit a straight line trend by the method of least squares to the following data

Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test?

Compute the consumer price index for 2015 on the basis of 2014 from the following data.

An Enquiry was made into the budgets of the middle class families in a city gave the following information.

What changes in the cost of living have taken place in the middle class families of a city?

From the following data, calculate the control limits for the mean and range chart.

The following data gives the average life(in hours) and range of 12 samples of 5lamps each. The data are

Construct control charts for mean and range. Comment on the control limits.

The following are the sample means and I ranges for 10 samples, each of size 5. Calculate; the control limits for the mean chart and range chart and state whether the process is in control or not.