Question

The number of hours spent studying and percentage marks for 5 students are tabulated below. Find the correlation coefficient using Karl Pearson's formula.

$\begin{array}{cc}\text{No. of hours}& \%\text{Marks}\\ 3& 75\\ 4& 85\\ 5& 80\\ 6& 82\\ 7& 88\end{array}$

• A. 0.685
• B. 0.735
• C. 0.825
• D. 0.935

Answer 1

The correct option is B

0.735

$\begin{array}{ccccc}{X}_i& Y_i& X_i^2& Y_i^2& X_i{Y}_i\\ 3& 75& 9& 5625& 225\\ 4& 85& 16& 7225& 340\\ 5& 80& 25& 6400& 400\\ 6& 82& 36& 6724& 492\\ 7& 88& 49& 7744& 616\\ \sum =25& \sum =410& \sum =135& \sum =33718& \sum =2073\end{array}$

$r=\frac{N{\sum }_{i=1}^n\left(X_i{Y}_i\right)–\left({\sum }_{i=1}^n{X}_i\right)\left({\sum }_{i=1}^n{Y}_i\right)}{\sqrt{N{\sum }_{i=1}^n{X}_i^2–({\sum }_{i=1}^n{X}_i{)}^2}\sqrt{N{\sum }_{i=1}^n{Y}_i^2–({\sum }_{i=1}^n{Y}_i{)}^2}}=\frac{115}{7.07\times 22.14}=0.735$