50% of items have characteristics A and B both, 35% have A, but not B, 25% have B but not A. Show that there must be some misprints in this report.

Suppose X and Y are the two variables having the correlation coefficient 0.85. The following are the values they have:

If two new variables X' and Y' are obtained by adding 50 to each value of X and 100 to each value of Y, respectively, calculate the correlation coefficient between X' and Y' using the above data. Also compare the results.

In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as 8X - 10Y + 70 = 0 and 20X - 9Y - 65 = 0. The standard deviation of X = 3, then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y

Can vaccination be regarded as a preventive measure for smallpox from the given data:

(i) Of 1482 persons in a locality exposed to smallpox, 368 in all were attacked, and

(ii) Of 1482 persons, 343 had been vaccinated and of these only 35 were attacked.

An investigation of 23713 households was made in an urban and rural mixed locality. Of these 1618 were farmers, 2015 well to do and 770 families were having at least one graduate. Of these graduate families 335 were those of farmers and 428 were well to do; also 587 well to do families were those of farmers and out of them only 156 were having at least one graduate. Obtain all the ultimate class frequencies.

Given the following data: 

 (i) r_12.3 (ii) r_13.2(iii) r _23.1 (iv) R_1.23

The following table shows the information as:

(i) the expected advertising expenditure of the company if sale is Rs. 125 lakhs, and

(ii) the expected sales of the company if the advertising expenditure is Rs 32 lakhs.

Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:

and

The value of Spearman's rank correlation coefficient of a set of non-repeating values was found to be 2/3. The sum of the squares of difference between the corresponding ranks was 55. Find the number of pairs.

The following is the distribution of age (in years) of 800 workers:

Find (i) Median, (ii) Quartile Deviation, and (iii) Coefficient of Quartile Deviation.

The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies Y, (Y+2), (Y-3) and (Y+6), respectively. If the arithmetic mean is 4.876, find the value of Y and write the whole series.

State whether the following statements are true or false and also give the reason in support of your answer:

(a) if  are the variate values  of two variables X and and their geometric means are Grand G₂, respectively, then geometric mean of  will be (G₁/G₂).

(b) If X and Y are two independent variables and the variables U=X+ Y and V= X-Y, then the

(c) If each value of X is divided by 2 and of Y is multiplied by 2, then b'yx will be same as byx.

(d) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.

(e) If

What is the relation of unit on y-axis with unit on x-axis in histogram.

Write any 10 principles of data visualisation.

Write whether the following data are discrete or continuous. Give reason in support of your answer.

i) Number of children in a family in a colony of 100 families.

Number of pages in each of the 50 books having some mistake.

Height of students of IGNOU who enrolled in 2021.

iv) Waiting time of metro when a person reaches metro station.

v) Monthly income of the family.

Write flow charts of Cramer rule and matrix method.

Find values of x, y and z given that

You are bound to use the matrix techniques to solve the given equations.

Evaluate the following integrals:

i) 

ii) 

Discuss the continuity and differentiability of the following function at x = 2/3:

If in a hall there are 10 randomly selected students then how many numbers of ways are there such that all of them have different birthday. Assume that all of them have their birthday in non-leap years.