Slope

Q. In a distance - time graph, zero slope implies the object is at rest.

1. False
2. True

Q.

Identify the correct statement(s) about the line of best fit.

1. It is unique for a set of data

2. It passes through all points in a dataset

3. It is the line for which the errors of the data values are the least

4. It is obtained by minimizing the algebraic sum of errors

Q.

The slope, M of the line of best fit for the bivariate frequency distribution in variables x and y is given by the formula

1. $M={\sum }_{i=1}^n\frac{(x_i-\overline{x})(y_i-\overline{y})}{(x_i-\overline{x}{)}^2}$

2. $M={\sum }_{i=1}^n\frac{(x_i-\overline{x})(y_i-\overline{y})}{(y_i-\overline{y}{)}^2}$

3. $M=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{{\sum }_{i=1}^n(y_i-\overline{y}{)}^2}$

4. $M=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}$

Q.

To find the line of best fit, which of the following is minimized?

1. ${\sum }_{i=1}^n(y_i-\widehat{y_i}{)}^2$

2. ${\sum }_{i=1}^n|y_i-\widehat{y_i}|$

3. ${\sum }_{i=1}^n(x_i-\widehat{x_i}{)}^2$

4. ${\sum }_{i=1}^n|x_i-\widehat{x_i}|$

Q.

Shreya was doing an experiment to find out the relationship between voltage (X) and current (Y). The values obtained by Shreya are tabulated below.

$\begin{array}{cc}Voltage\left(X\right)& Current\left(Y\right)\\ 2& 3.5\\ 3& 5.5\\ 4& 8\\ 5& 9.5\\ 6& 12\\ 7& 14.5\\ 8& 16\end{array}$

Find the line of best fit for this data.

1. y = 2.05x -0.45

2. y = 2.125x - 0.765

3. y = 2x

4. y= 1.95x +0.65

Q.

The following table contains the heights and weights of a sample of 5 women from a room. Find the line of best fit.

$\begin{array}{cc}Height(X,cm)& Weight(Y,kg)\\ 150& 54\\ 160& 58\\ 170& 63\\ 175& 65\\ 180& 70\end{array}$

1. $y=0.42x-36.24$

2. $y=0.63x-15.5$

3. $y=0.51x-23.17$

4. $y=0.36x-41.65$

Q.

The following table contains the quantity of goods supplied by a firm at different prices. Use interpolation to find what quantity of goods would the firm supply at a price of Rs 85.

$\begin{array}{cc}Price\left(X\right)& Quantity\left(Y\right)\\ 25& 19\\ 50& 32\\ 75& 39\\ 100& 48\\ 125& 63\\ 150& 68\end{array}$

1. 42

2. 46

3. 44

4. 47

Q.

The following table contains the heights and weights of a sample of 5 women from a room. Find the approximate weight corresponding to 165 cm using interpolation.

$\begin{array}{cc}Height(X,cm)& Weight(Y,kg)\\ 150& 54\\ 160& 58\\ 170& 63\\ 175& 65\\ 180& 70\end{array}$

1. 61.5 kg

2. 62 kg

3. 61 kg

4. 59.5 kg

Q.

Find the equation of the line of best fit for the following data.

$\begin{array}{cc}X& Y\\ 2& 5\\ 5& 7\\ 6& 8\\ 8& 11\\ 10& 12\\ 12& 16\\ 14& 17\end{array}$

1. y=1.07x +2.15

2. y =1.07x + 3.35

3. y=2.07x +2.15

4. y =2.07x + 3.35

Q.

The following table contains the placement statistics for JKL institute of technology. The first column contains the CGPA or grade of the students and the second column contains the average salary in lakhs per annum. Find the average salary corresponding to 8.5 CGPA using linear interpolation.

$\begin{array}{cc}CGPA\left(X\right)& Salary\left(Y\right)\\ 5& 2.5\\ 6& 4\\ 6.5& 4.5\\ 7& 6\\ 7.5& 7.5\\ 8& 9\\ 9& 11\end{array}$

1. 8.8 lakhs per annum

2. 9.24 lakhs per annum

3. 9.72 lakhs per annum

4. 10.12 lakhs per annum