Additional Problems - Chapter 9 Applied Statistics 12th Maths Guide Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Additional Problems
Choose the correct answer.
Question 1.

Answer:
(a) - (iv)
(b) - (iii)
(c) $-$ (i)
(d) - (ii)
Question 2.
The secular trend can be measure by
(a) 4 methods
(b) 1 method
(c) 2 methods
(d) none of these
Answer:
(a) 4 methods
Question 3.
Method of simple averages is used to measure
(a) Secular trend
(b) Irregular variation
(c) Seasonal variation
(d) Cyclic variation
Answer:
(c) Seasonal variation
Question 4.
Increase in the number of patients in the hospital due to heatstroke is
(a) Secular trend
(b) Irregular variation
(c) Seasonal variation
(d) Cyclic variation
Answer:

(c) Seasonal variation

Question 5.
In time series seasonal variations can occur within a period of
(a) 4 years
(b) 3 years
(c) one year
(d) 9 years
Answer:
(c) one year
Question 6.
Fill in the blanks.
1. The method of moving averages is used to find the ____
2. Most frequently used mathematical model of a time series is ________
3. The sale of air condition increases during summer is a ______
4. The fire in a factory is an example of ____________
5. The best-fitting trend is one in which the sum of squares of residuals is __________
Answer:
1. Secular trend
2. Multiplicative model
3. Seasonal variation
4. Irregular variation
5. Least
Question 7.
True or False
1. An index number is used to measure changes in a variable over time.
2. The ratio of a new price to the base year price is called the price relative.
3. The Laspeyre's and Paasche index numbers are examples of weighted quantity index only.
4. $\frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100$ is Laspeyre's quantity index.
5. Laspeyre's price index regards the base year quantities as fixed.
Answer:
1. True
2. True
3. False
4. False
5. True

Question 8.
Index for base period is always taken as
(a) 100
(b) 1
(c) 200
(d) 0
Answer:
(a) 100
Question 9.
Consumer price index indicates
(a) Rise
(b) Fall
(c) both (a) \& (b)
(d) neither (a) \& (b)
Answer:
(c) both (a) \& (b)
Question 10.
The purchasing power of money can be accessed through
(a) simple index
(b) Fisher's index
(c) Consumer price index (CPI)
(d) Volume index
Answer:
(c) Consumer price index (CPI)
Question 11.
For consumer price index, price quotations are collected from
(a) Fair price shops
(b) Government depots
(c) Retailers
(d) Whole-sale dealers
Answer:
(c) Retailers
Question 12 .
The aggregative expenditure method and family budget method always give
(a) Different results
(b) Approximate results
(c) Same results
(d) None of these
Answer:
(c) Same results

Question 13.
The Federal Bureau of statistics prepares
(a) The wholesale price index
(b) CPI
(c) Sensitive price indicator
(d) All the above
Answer:
(d) All the above
Question 14.
Paasche's price index number is also called
(a) Base year weighted
(b) Current year weighted
(c) Simple aggregative index
(d) Consumer price index
Answer:
(b) Current year weighted
Question 15.
Index number calculated by Fisher's formula is ideal because it satisfies
(a) Circular test
(b) Factor reversal test
(c) Time reversal test
(d) All of the above
Answer:
(d) All of the above
2 Mark Questions
Question 1.
From the data given below calculate seasonal Indices:

Solution:

Grand Average $=\frac{42.4+36.2+37.8+40.2}{4}=39.15$
S.I for I quarter $=\frac{42.4}{39.15} \times 100=108.3$
S.I for II quarter $=\frac{36.2}{39.15} \times 100=92.46$
S.I for III quarter $=\frac{37.8}{39.15} \times 100=96.55$
S.I for IV quarter $=\frac{40.2}{39.15} \times 100=102.68$
Question 2.
Using 3-year moving averages, determine the trend values from the following data.

Solution:

Question 3.
A company estimates its average monthly sales in a particular year to be Rs. $2,00,000$. The seasonal indices of the sales data are given below. Draw a monthly sales budget for the company.

Solution:

$\begin{aligned}
\text { Seasonal Index }(\text { S.I }) & =\frac{\text { Monthly Average }}{\text { General average }} \times 100 \\
\Rightarrow \quad \text { M.A } & =\frac{\text { S.I. } \times \text { G.A }}{100}=\frac{\text { S.I } \times 2,00,000}{100}=S . I \times 2000
\end{aligned}$

Question 4.
Calculate the index for the data when the average percentage increases in the prices of items and weights are given. Food 15, clothing 3, Rent 4, Fuel 2, Miscellaneous 1, the percentage increases are $32,54,47,78$ and 58 .
Solution:

Cost of living index number $=\frac{\sum \mathrm{WI}}{\sum \mathrm{W}}=\frac{3544}{25}=141.76$
3 and 5 Marks Questions
Question 1.
Using Fisher's Ideal Formula, compute price and quantity index number for 1984 with 1982 as the base year, from the given information.

Solution:
Fisher's ideal index number for price
$
\begin{aligned}
& =\sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times 100 \\
& =\sqrt{\frac{97}{116} \times \frac{117}{140}} \times 100=83.6
\end{aligned}
$
Fisher's ideal index number for quantity
$
\begin{aligned}
& =\sqrt{\frac{\sum q_1 p_0}{\sum q_0 p_0} \times \frac{\sum q_1 p_1}{\sum q_0 p_1}} \times 100 \\
& =\sqrt{\frac{140}{116} \times \frac{117}{97}} \times 100=120.6
\end{aligned}
$
Question 2.
Using the following data, compute Fisher's Ideal price index number for the current year.

Solution:

Fisher's Ideal index number for price
$
=\sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times 100=\sqrt{\frac{392}{308} \times \frac{348}{288}} \times 100=124.0
$
Question 3.
Calculate the cost of living Index number from the following data.

Solution: 

Cost of living index number $=\frac{\sum P W}{\sum W}=\frac{1568.75}{12}=130.73$
Question 4.
Given below are the values of the sample mean $(\bar{X})$ and the range $(\mathrm{R})$ for ten samples of size 5 each. Find the control charts and comment on the state of the process.

Use $\mathrm{A}_2=0.58, \mathrm{D}_3=0, \mathrm{D}_4=2.115$
Solution:

$
\overline{\bar{X}}=\frac{442}{10}=44.2 \quad \bar{R}=\frac{58}{10}=5.8
$
The control limits for mean $\overline{\mathrm{X}}$ chart are
$
\begin{aligned}
& \mathrm{LCL}=\overline{\bar{X}}-\mathrm{A}_2 \overline{\mathrm{R}}=44.2-(0.58)(5.8)=40.836 \\
& \mathrm{CL}=\overline{\bar{X}}=44.2 \\
& \mathrm{UCL}=\overline{\bar{X}}+\mathrm{A}_2 \overline{\mathrm{R}}=44.2+(0.58)(5.8)=47.564
\end{aligned}
$
The control limits for $\mathrm{R}$ chart are
$
\begin{aligned}
\mathrm{LCL} & =\mathrm{D}_3 \overline{\mathrm{R}}=0(5.8)=0 \\
\mathrm{CL} & =\overline{\mathrm{R}}=5.8 \\
\mathrm{UCL} & =\mathrm{D}_4 \overline{\mathrm{R}}=(2.115)(5.8)=12.261
\end{aligned}
$
We observe that all the sample range values are within the control limits values of $R$ chart, But two values of the sample $\bar{X}$ (i.e) 37, 37 lies below the LCL and 49, 51 lie above the UCL. So the statistical process is out of control.
Question 5.
Fit a straight line trend equation by the method of least squares and estimate the trend values.

Solution:
Let $Y_{\mathrm{t}}=\mathrm{a}+\mathrm{bx}$ be the trend line.
Let $\mathrm{X}=\frac{x-1964.5}{0.5}, \mathrm{X}$ denotes year.

$
a=\frac{\sum \mathrm{Y}}{n}=\frac{734}{8}=91.75 \quad b=\frac{\sum \mathrm{XY}}{\sum \mathrm{X}^2}=\frac{210}{168^{\circ}}=1.25
$
So the trend line is $\mathrm{Y}_{\mathrm{t}}=91.75+1.25 \mathrm{X}$
(i.e) $\mathrm{Y}_{\mathrm{t}}=91.75+1.25\left(\frac{x-1964.5}{0.5}\right)$
When $\mathrm{x}=1961, \mathrm{Y}_{\mathrm{t}}=91.75-7(1.25)=83$
When $\mathrm{x}=1962, \mathrm{Y}_{\mathrm{t}}=91.75-5(1.25)=85.5$
We can find other values similarly.