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There are 200 individuals with a skin disorder, 120 has been exposed to chemical $C_1$, 50 to chemical $C_2$ and 30 to both the chemicals $C_1$ and $C_2$, find the number of individuals exposed to

(i) chemical $C_1$ or chemical $C_2$.

(ii) chemical $C_1$ but not chemical $C_2$.

(iii) chemical $C_2$ but not chemical $C_1$.

An original frequency table with mean 11 and variance 9.9 was lost but the following table derived from it was found. Construct the original table.

$\begin{array}{cccccc}\text{value of deviation (d)}& -2& -1& 0& 1& 2\\ \text{Freuency(f)}& 1& 6& 7& 4& 2\end{array}$

From the following data, compute the coefficient of correlation between X and Y series.
$$\begin{array}{ccc}& \text{X series}& \text{Y Series}\\ \text{Number of items}& 6& 6\\ \text{Arithmetic mean}& 350& 138\\ \text{Squares of deviations from mean}& 19& 94\end{array}$$
Summation of product of deviations of X and Y series from their respective arithmetic mean= 41.

Give the formula of calculating median in frequency distribution.

Which of the following is incorrect?

Construct index number of Paasche's method:

$\begin{array}{ccccc}\text{Commodities}& \text{Year 2005}& \text{Year 2005}& \text{Year 2006}& \text{Year 2006}\\ & \text{Price}& \text{Quantity}& \text{Price}& \text{Quantity}\\ \text{A}& 2& 8& 4& 6\\ \text{B}& 5& 10& 6& 5\\ \text{C}& 4& 14& 5& 10\\ \text{D}& 2& 19& 2& 13\end{array}$

The item having the highest weight in consumer price index for industrial workers in 2017 is____.

In a singing competition, two judges rank the seven contestants as follows:

$\begin{array}{cccccccc}\text{Judge 1}& 5& 4& 7& 3& 1& 2& 6\\ \text{Judge 2}& 6& 5& 2& 1& 3& 4& 7\end{array}$

Calculate the coefficient of rank correlation.

Calculate the weighted aggregative index number for the following considering the base period consumption as a standard:

$\begin{array}{ccccc}& P_0& Q_0& P_1& Q_1\\ A& 1& 12& 3& 15\\ B& 6& 10& 8& 11\\ C& 3& 9& 4& 7\\ D& 12& 15& 19& 20\\ E& 8& 25& 13& 18\end{array}$

All prices are in dollars.

Two ladies were asked to rank ten different types of cell phones. The ranks given by them are given below :

$\begin{array}{ccccccccccc}\text{Cell Phone}& \text{A}& \text{B}& \text{C}& \text{D}& \text{E}& \text{F}& \text{G}& \text{H}& \text{I}& \text{J}\\ \text{Tina}& 1& 6& 3& 9& 5& 2& 7& 10& 8& 4\\ \text{Rita}& 6& 8& 3& 7& 2& 1& 5& 9& 4& 10\end{array}$

Calculate Spearman's rank correlation coefficient.

What are the factors does reliability of sampling data depend on?

'Use of open-end classes should be encouraged'. Comment.

Suppose the wage of an industrial worker follows a path given by S $=x^2$ and inflation rate during the same time is given by $I=e^x$ where x is the time in months. What can you say about his standard of living provided all other factors remain constant? Give reasons behind your observations.

Which one of these is unaffected by outliers?

a. Mean

b. Inter-quartile Range

c. Standard Deviation

d. Range

In the following table is given, the number of companies belonging to two areas A and B according to the amounts of profits earned by them. Draw their Lorenz curve.

$\begin{array}{ccc}\text{Profits Earned (Rs in 000)}& \text{Area A}& \text{Area B}\\ 6& 6& 2\\ 25& 11& 38\\ 60& 13& 52\\ 84& 14& 28\\ 105& 15& 38\\ 150& 17& 26\\ 170& 10& 12\\ 400& 14& 4\end{array}$

Calculate coefficient of variation of the following series:
$$\begin{array}{ccccccccccc}\text{S.No.}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ \text{Marks}& 53& 58& 25& 30& 54& 42& 32& 48& 46& 52\end{array}$$

Define index number.

Arjun has calculated the Spearman's rank coefficient for 6 students based on their scores in economics and mathematics to be 0.69. Three students had the same score in economics and 2 students had the same score in Mathematics. Arjun forgot to add the correction factor in his calculations. What will be the corrected Rank coefficient?

The weighted aggregative index number for the following table is given as 166.31 considering Paasche’s method. Find the approx.value of m.

$\begin{array}{ccccc}\text{Commodity}& & \text{Base Period}& & \text{Current Period}\\ & \text{Price (P0) (In dollars)}& \text{Quantity (Q0)}& \text{Price (P1) (In dollars)}& \text{Quantity (Q1)}\\ H& 1& 7& 3& 25\\ I& 10.5& 10& 7& 11\\ J& m& 8& 4& 12\\ K& 7& 25& 14& 30\\ L& 15& 13& 22& 18\end{array}$

What is meant by inferential statistics?

If the mean and variance of the observations $x_1,x_2,x_3,\cdots ,x_n$ are $\overline{x}$ and ${\sigma }^2$ respectively and a be a nonzero real number, then show that the mean and variance of $a{x}_1,a{x}_2,a{x}_3,\cdots .a{x}_n$ are $\overline{ax}$ and $a^2{\sigma }^2$ respectively.

If x represents the encouragement points given to a punctual student and y represents the points given for irregularity of a student, then find how many points are fixed for each, if x and y are connected by the relation, $\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i?$

Students getting y point are lacking which value system ?

Explain the 'exclusive' and 'inclusive' methods used in classification of data.

'Statistics are figures, but all figures are not statistics'. Justify the statement.

A bag contains $30$ white balls and $10$ red balls. $16$ are drawn one by one randomly from the bag with replacement. If $X$ be the number of white balls drawn, then $\left(\frac{\text{mean of X}}{\text{standard deviation of X}}\right)$ is equal to :

What is the principal drawback of mean deviation as a measure of dispersion?

Find the mean, variance and standard deviation for the following data using short cut method:

$\begin{array}{cccccccccc}{x}_i& 60& 61& 62& 63& 64& 65& 66& 67& 68\\ f_1& 2& 1& 12& 29& 25& 12& 10& 4& 5\end{array}$

The relative importance of the items is accounted for in___.

The marks of some students were listed from total marks of $75.$ The standard deviation of marks was found to be $9.$ Subsequently, the marks were raised to a maximum of $100$, and variance of new marks was calculated. The new variance is

What is a class interval? How are the magnitude of the class interval and class limits determined?

Find the mean deviation about the mean for the data in Exercises 9 to 10 $\begin{array}{ccccccccc}\text{Income per day}& 0-100& 100-200& 200-300& 300-400& 400-500& 500-600& 600-700& 700-800\\ \text{Number of persons}& 4& 8& 9& 10& 7& 5& 4& 3\end{array}$

Define Marginal Physical Product.

Which of the following is the correct formula for the correlation coefficient, r?

What do you mean by 'montonic preferences'?

Which of the following is a contingent function of money?

Calculate weighted index number for 2010 by weighted aggregative method and weighted average of relative method for the following data:

$\begin{array}{cccc}\text{Items}& \text{Weights}& \text{Prices in 2011}& \text{Prices in 2012}\\ A& 10& 100& 161\\ B& 7& 200& 210\\ C& 15& 50& 60\\ D& 9& 20& 30\\ E& 10& 10& 14\end{array}$

In a city, 45 families were surveyed for the number of domestic appliances they used. Prepare a frequency array based on their replies as recorded below.

$\begin{array}{ccccccccccccccc}1& 3& 2& 2& 2& 2& 1& 2& 1& 2& 2& 3& 3& 3& 3\\ 3& 3& 2& 3& 2& 2& 6& 1& 6& 2& 1& 5& 1& 5& 3\\ 2& 4& 2& 7& 4& 2& 4& 3& 4& 2& 0& 3& 1& 4& 3\end{array}$

What are the limitations of Diagrammatic Presentation?

Which measure of dispersion is the best and how?

A system undergoes a process in which system releases 200 J heat and workdone by the surroundings is 300 J. Change in internal energy of the system is

The mean and variance of the heights and weights of the students of a class are given below.

$\begin{array}{ccc}& \text{Height}& \text{Weight}\\ \text{Mean}& \text{160 cm}& \text{50.4 kg}\\ \text{Variance}& 116.64c{m}^2& 17.64k{g}^2\end{array}$

Show that the weights are more variable than heights.

Convert $\frac{48}{25}$ to decimal form.

Comment upon the degree of elasticity of demand for Good X, in the following given situations, if the price of the commodity rises from Rs. 5 per unit ot Rs. 7 per unit and the quantity demanded falls from 20 units to 16 units:
(i) Using the total household expenditure method,
(ii) Using proportionate method.

Explain any two advantages and disadvantages of textual presentation.

Explain the concept of 'Marginal Rate of Substitution' with the help of a numerical example. Describe its behaviour along an indifference curve.

On which axis, dependent variables are represented?

In the following question, there is a blank in each sentence. Four alternatives are suggested for each blank. Choose the correct one.
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