A survey was conducted in your city. Given is the following sample data containing a person's age and their corresponding income. Find out whether the increase in age has an effect on income using the correlation coefficient formula.

**Age**
25
30
36
43
**Income**
30000
44000
52000
70000

**Age****Income**## Important Questions on Interpreting Categorical and Quantitative Data

Find correlation coefficient:

$X$ | $5$ | $4$ | $3$ | $2$ | $1$ |

$Y$ | $1$ | $2$ | $3$ | $4$ | $5$ |

What is the correlation by the following scatter diagram?

Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.(Answer up to three decimal values)

$\begin{array}{|cccccccccc|}\hline x& 9& 8& 7& 6& 5& 4& 3& 2& 1\\ y& 15& 16& 14& 13& 11& 12& 10& 8& 10\\ \hline\end{array}$

If two variables oppose each other then the correlation will be _____.

Calculate the Karl Pearson’s correlation coefficient between the marks in statistics and mathematics of $6$students.(Answer up to three decimal places).

$\begin{array}{|lcccccc|}\hline \text{Student}& 1& 2& 3& 4& 5& 6\\ \text{Statistics}& 7& 4& 6& 9& 3& 8\\ \text{Mathematics}& 8& 5& 4& 8& 3& 6\\ \hline\end{array}$

Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.(Answer up to two decimal values)

$\begin{array}{|cccccccccc|}\hline x& 9& 8& 7& 6& 5& 4& 3& 2& 1\\ y& 15& 16& 14& 13& 11& 12& 10& 8& 9\\ \hline\end{array}$

Consider the following statements with regard to correlation coefficient $r$ between random variables $x$ and $y$.

$\mathrm{I}.$ $r=+1$ or $-1$ means there is a linear relationship between $x$ and $y$.

$\mathrm{II}.$ $-1\le r\le 1$ and ${r}^{2}$ is a measure of the linear relationship between the variables.

Which of the above statement(s) is$/$are correct $?$