Question

a sample of survey data shows the age and height of 15 randomly chosen people. what is the correlation coefficient of this data? a 0.82 b 0.21 c 0.00 d 0.06

Explanation:

Step1: Input data into calculator

Input the age (x - values) and height (y - values) from the table into a graphing calculator or statistical software.

Step2: Calculate correlation coefficient

Use the correlation coefficient function (\(r\) - value function) in the graphing calculator or software. For a set of data points \((x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)\), the formula for the sample correlation coefficient \(r=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2\sum_{i = 1}^{n}(y_i-\bar{y})^2}}\), where \(\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i\) and \(\bar{y}=\frac{1}{n}\sum_{i=1}^{n}y_i\). But using technology (like Desmos) is more efficient. When we input the data:
Age values \(x=\{33,38,36,27,81,86,37,55,18,49,43,60,61,68,19,51\}\)
Height values \(y = \{66,66,62,61,66,71,67,70,73,68,70,61,62,61,66,72\}\)
After inputting into Desmos (or a similar statistical tool), we find that \(r\approx0.21\)

Answer:

B. \(0.21\)