HSC Commerce: Marketing and Salesmanship इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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')

Write the conjugates of the following complex numbers: 3 + i

Write the conjugates of the following complex numbers: 3 – i

Write the conjugates of the following complex numbers: `-sqrt(5) - sqrt(7)  "i"`

Write the conjugates of the following complex number:

`-sqrt(-5)`