Solve your IGNOU Doubts

Question:

Board of Directors of Labour Union wishes to sample the opinion of its members before submitting a change in its contribution at a forthcoming annual meeting. Questionnaires are sent to a random sample of 200 members in three union locals. The results of the survey are as follows:

	Union Locals
Reaction	A	B	C	Total
Favour Change	35	45	20	100
Against Change	15	25	16	56
No Response	10	10	24	44
Total	60	80	60	200

Determine the amount of association between the Union locals and their reactions using coefficient of contingency and interpret the result.

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Question:

Calculate the first, second and third quartile for the following data:

Class:		Below 30		30-40		40-50		50-60	60-70		70-80		80 and above
Frequency:		69		167		207		65	58		27		10

Also find the quartile deviation and coefficient of quartile deviation.

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Question:

Fit an exponential curve of the form $Y = ab^X$ to the following data:

X:	1	2		3	4	5		6	7		8
Y:	1.0	1.2		1.8	2.5	3.6		4.7	6.6		9.1

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Question:

A statistician wanted to compare two methods A and B of teaching. He selected a random sample of 22 students. He grouped them into 11 pairs so that the students in pair have approximately equal scores on an intelligence test. In each pair one student was taught by method A and the other by method B and examined after the course. The marks obtained by both methods are given as:

Methods	1	2	3	4	5	6	7	8	9	10	11
Method A	24	29	19	14	30	19	27	30	20	28	11
Method B	37	35	16	26	23	27	19	20	16	11	21

Find the rank correlation coefficient.

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Question:

If a, b, c, d are constants, then show that the coefficient of correlation between ax+b and cy+d is numerically equal to that between x and y.

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Question:

A researcher collects the following information for two variables x and y: n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, $\sigma_x = 4$ and $\sigma_y = 5$ Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30) whereas the correct values were (26, 35). Find the correct value of r(x, y)

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Question:

The equations of two regression lines are given as follows:

$4x - 5y + 30 = 0$

$20x-9y-107 = 0$

Calculate (i) regression coefficients, $b_{yx}$ and $b_{xy}$ ; (ii) correlation coefficient r(x, y); (iii) Mean of X and Y; and (iv) the value of $\sigma_y$ if $\sigma_x = 3$ .

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Question:

Mean and Standard deviation of 18 observations are found to be 7 and 4, respectively. On comparing the original data, it was found that an observation 12 was miscopied as 21 in the calculations. Calculate correct mean and standard deviation.

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Question:

The frequency distribution of the marks obtained by the 25 students each of the two sections is given as follows:

Marks:	10-20	20-30	30-40	40-50	50-60
Section A:	2	5	10	5	3
Section B:	3	7	8	5	2

Find which section is more consistent.

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Question:

If AM and GM of two numbers are 30 and 18, respectively, find the numbers.

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Question:

Find the missing information from the following data:

	Group I	Group II	Group III	Combined
Number	50	?	90	200
Standard Deviation	6	7	?	7.746
Mean	113	?	115	116

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Question:

State whether the following statements are True or False and also give the reason in support of your answer.
a) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.
b) Mean deviation is least when calculated from the median.
c) The correlation coefficient between x and (a – x) is –1.
d) The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively.
e) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.

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Question:

Draw a histogram for the following data:

Wages	40 – 49		50 – 69		70 – 99	100 – 109	110 – 119
No of workers	2		20		60	35	4

Also draw frequency polygon in the same graph.

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Question:

Find the values of a and b, if the function f given below is continuous at x = 2

$f(x) = \begin{Bmatrix} a+b, & x<2\\ a+bx+4, & x=2\\ 5, & x>2 \end{Bmatrix}$

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Question:

Draw a box plot with whisker, +ve sign and outliers for the following data: 42, 37, 28, 23, 32, 25, 26, 39, 38, 41, 22, 38, 21, 31, 26, 36, 42, 52, 50, 47, 24, 53, 28

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Question:

What do you mean by primary data and secondary data? Also give an example in each case.

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Question:

Prove that $\begin{vmatrix} a & b &c \\ b & c &a \\ c &a & b \end{vmatrix} = (a+b+c)(ab+bc+ca-a^2-b^2-c^2)$

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Question:

Evaluate the following:

a). $\int x^2e^{2x}dx$

b). $\frac{dy}{dx}$ , where $y = (4x+5)^4(9x+4)^5$

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Question:

If the universal set is $U = \left \{ 1,2,3,4,5,6,7,8 \right \}$ and $A = \left \{ 2, 3, 6, 7 \right \}$ , $B = \left \{ 4, 6, 8 \right \}$ , $C = \left \{ 6, 7,8 \right \}$ are the subsets of $U$ , then verify
a) De-Morgan’s laws
b) left distributive law

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Question:

Arrange the numbers 49, 36, 42, 19, 22, 27, 14, 13, 24, 48, 23, 28, 17, 42, 39, 45, 22, 24, 17, 41, 18, 42, 38, 43, 11, 27, 36, 13, 40, 30, 24, 10, 18, 47, 18, 19, 23, 12, 27 in stretched stemand-leaf display that has single-digit starting parts and leaves, but has stem width of 5.

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