HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):

If r = 0.6, Estimate x when y = 16 and y when x = 10

Mean of x = `barx = square`

Mean of y = `bary = square`

b_xy = `square/square`

b_yx = `square/square`

Regression equation of x on y is `(x - barx) = "b"_(xy)  (y - bary)`

∴ Regression equation x on y is `square`

Regression equation of y on x is `(y - bary) = "b"_(yx)  (x - barx)`

∴ Regression equation of y on x is `square`

For certain bivariate data on 5 pairs of observations given:

∑x = 20, ∑y = 20, ∑x² = 90, ∑y² = 90, ∑xy = 76 then b_xy = ______.

The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.

`sum(x_i - barx)(y_i - bary)` = 1170

For a bivariate data:

`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

Find: 

1. b_yx
2. b_xy
3. Correlation coefficient between x and y.

Following table shows the all India infant mortality rates (per '000) for years 1980 to 2010:

Fit the trend line to the above data by the method of least squares.

For a bivariate data `barx = 10`, `bary = 12`, V(X) = 9, σ_y = 4 and r = 0.6
Estimate y when x = 5

Solution: Line of regression of Y on X is

`"Y" - bary = square ("X" - barx)`

∴ Y − 12 = `r.(σ_y)/(σ_x)("X" - 10)`

∴ Y − 12 = `0.6 xx 4/square ("X" - 10)`

∴ When x = 5

Y − 12 = `square(5 - 10)`

∴ Y − 12 = −4

∴ Y = `square`

Obtain the trend values for the data in using 4-yearly centered moving averages.

Moving averages are useful in identifying ______. 

Which component of time series refers to erratic time series movements that follow no recognizable or regular pattern?

Fill in the blank :

_______ component of time series is indicated by a smooth line.

The simplest method of measuring trend of time series is ______.

Solve the following problem:

Following data shows the number of boxes of cereal sold in years 1977 to 1984.

Fit a trend line to the above data by graphical method.

Which of the following can’t be a component of a time series?

Choose the correct alternative:

The following trend line equation was developed for annual sales from 1984 to 1990 with 1984 as base or zero year.

Y = 500 + 60X (in 1000 ₹). The estimated sales for 1984 (in 1000 ₹) is

The complicated but efficient method of measuring trend of time series is ______

State whether the following statement is True or False: 

Moving average method of finding trend is very complicated and involves several calculations

Following table shows the amount of sugar production (in lac tons) for the years 1971 to 1982

Fit a trend line by the method of least squares

Obtain the trend values for the data, using 3-yearly moving averages

Use the method of least squares to fit a trend line to the data given below. Also, obtain the trend value for the year 1975.