1. **State the problem:** We want to find the Pearson product-moment correlation coefficient $r$ between the years of higher education (variable $X$) and monthly salary in thousands (variable $Y$) for 10 persons. 2. **Given data:** \begin{array}{ccc} \text{Person} & X (\text{Years}) & Y (\text{Salary in thousands}) \\ 1 & 4 & 21.4 \\ 2 & 4 & 18.7 \\ 3 & 5 & 17.5 \\ 4 & 8 & 32 \\ 5 & 1 & 12.6 \\ 6 & 5 & 25.3 \\ 7 & 10 & 35.5 \\ 8 & 4 & 17.3 \\ 9 & 8 & 33.8 \\ 10 & 1 & 14 \end{array} 3. **Calculate the means:** $$ \bar{X} = \frac{4+4+5+8+1+5+10+4+8+1}{10} = \frac{50}{10} = 5 $$ $$ \bar{Y} = \frac{21.4+18.7+17.5+32+12.6+25.3+35.5+17.3+33.8+14}{10} = \frac{228.1}{10} = 22.81 $$ 4. **Calculate components for $r$:** Calculate sums: $\sum (X_i - \bar{X})(Y_i - \bar{Y})$, $\sum (X_i - \bar{X})^2$, and $\sum (Y_i - \bar{Y})^2$. \begin{array}{cccccc} X_i & Y_i & X_i - \bar{X} & Y_i - \bar{Y} & (X_i - \bar{X})(Y_i - \bar{Y}) & (X_i - \bar{X})^2 \\ 4 & 21.4 & -1 & -1.41 & 1.41 & 1 \\ 4 & 18.7 & -1 & -4.11 & 4.11 & 1 \\ 5 & 17.5 & 0 & -5.31 & 0 & 0 \\ 8 & 32 & 3 & 9.19 & 27.57 & 9 \\ 1 & 12.6 & -4 & -10.21 & 40.84 & 16 \\ 5 & 25.3 & 0 & 2.49 & 0 & 0 \\ 10 & 35.5 & 5 & 12.69 & 63.45 & 25 \\ 4 & 17.3 & -1 & -5.51 & 5.51 & 1 \\ 8 & 33.8 & 3 & 11.0 & 33.0 & 9 \\ 1 & 14 & -4 & -8.81 & 35.24 & 16 \end{array} Sum these values: $$ S_{xy} = \sum (X_i - \bar{X})(Y_i - \bar{Y}) = 211.13 $$ $$ S_{xx} = \sum (X_i - \bar{X})^2 = 78 $$ Calculate $S_{yy} = \sum (Y_i - \bar{Y})^2$: \begin{array}{cc} (Y_i - \bar{Y})^2 \\ 1.9881 \\ 16.8921 \\ 28.1961 \\ 84.4561 \\ 104.2441 \\ 6.2001 \\ 161.0761 \\ 30.3601 \\ 121.0 \\ 77.6161 \end{array} Sum: $$ S_{yy} = 631.03 $$ 5. **Calculate Pearson's correlation coefficient:** $$ r = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}} = \frac{211.13}{\sqrt{78 \times 631.03}} = \frac{211.13}{\sqrt{49220.34}} = \frac{211.13}{221.86} \approx 0.952 $$ 6. **Interpret the result:** An $r$ value of approximately $0.952$ indicates a very strong positive linear relationship between years of higher education and monthly salary in thousands. This means that generally, more years of higher education correspond to higher salaries. **Final answer:** $$ r \approx 0.952 $$