HSC Commerce: Marketing and Salesmanship ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Following data gives the coded price (X) and demand (Y) of a commodity.

Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y. Also find conditional frequency distribution of Y when X is less than 10

Following data gives the age in years and marks obtained by 30 students in an intelligence test.

Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20, … etc. for age and 10 – 20, 20 – 30, … etc. for marks. Find conditional frequency distribution of marks obtained when the age of students is between 20 – 22.

Following data gives Sales (in Lakh ₹) and Advertisement Expenditure (in Thousand ₹) of 20 firms. (115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68) Conditional frequency distribution of Sales when the advertisement expenditure is between 64 – 66 (Thousand ₹)

Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.
(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)
Conditional frequency distribution of advertisement expenditure when the sales are between 125 – 135 (lakh Rs.)

Prepare a bivariate frequency distribution for the following data, taking class intervals for X as 35 – 45, 45 – 55, …. etc and for Y as 115 – 130, 130 – 145, … etc. where X denotes the age in years and Y denotes blood pressure for a group of 24 persons.
(55, 151) (36, 140) (72, 160) (38, 124) (65, 148) (46, 130) (58, 152) (50, 149) (38, 115) (42, 145) (41, 163) (47, 161) (69, 159) (60, 161) (58, 131) (57, 136) (43, 141) (52, 164) (59, 161) (44, 128) (35, 118) (62, 142) (67, 157) (70, 162)
Also, find Conditional frequency distribution of Y when X ≤ 45.

Two series of x and y with 50 items each have standard deviations of 4.8 and 3.5 respectively. If the sum of products of deviations of x and y series from respective arithmetic means is 420, then find the correlation coefficient between x and y.

Find the number of pairs of observations from the following data,
r = 0.15, `sigma_"y"` = 4, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 12, `sum("x"_"i" - bar"x")^2` = 40.

Given that r = 0.4, `sigma_"y"` = 3, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 108, `sum("x"_"i" - bar"x")^2` = 900. Find the number of pairs of observations.

Given the following information, `sum"x"_"i"^2` = 90, `sum"x"_"i""y"_"i"` = 60, r = 0.8, `sigma_"y"` = 2.5, where x_i and y_i are the deviations from their respective means, find the number of items.

A sample of 5 items is taken from the production of a firm. Length and weight of 5 items are given below. [Given : `sqrt(0.8823)` = 0.9393]

Calculate the correlation coefficient between length and weight and interpret the result.

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between 2x and y

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between `"x"/2` and y

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x and 3y

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x – 5 and y – 3

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x + 7 and y + 9

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between `("x" - 5)/7` and `("y" - 3)/8`?

In the calculation of the correlation coefficient between the height and weight of a group of students of a college, one investigator took the measurements in inches and pounds while the other investigator took the measurements in cm. and kg. Will they get the same value of the correlation coefficient or different values? Justify your answer.

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩B') = 5, find: n(A ∩ B)

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5, find: n(A' ∩ B)

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5,  find: n(A ∩ B')