Question

a group of persons filled in a questionnaire their age and the number of states they visited. the results are recorded in the table below.
bivariate age and
number of states
visited

age	states visited
20	22
19	17
36	5
27	7
52	37
47	14
53	32
37	22

-0.6
1.3
0.6
-1.3

Explanation:

Step1: Recall Correlation Coefficient Range

The correlation coefficient \( r \) ranges between \(-1\) and \( 1 \), so options \( 1.3 \) and \(-1.3\) are invalid (since they are outside \([-1, 1]\)).

Step2: Analyze Trend (Positive/Negative)

As age increases, the number of states visited generally increases (e.g., 19→5, 20→22; 36→5 (outlier), but overall trend: 19,20,19,36,27,52,47,53,37 – as age rises, states visited (5,22,17,5,7,37,14,32,22) shows a positive trend (ignoring the outlier at age 36). So \( r \) should be positive, eliminating \(-0.6\).

Step3: Determine Valid Positive Value

Among remaining options, \( 0.6 \) is positive and within \([-1, 1]\), matching the positive trend (after accounting for the outlier, the linear relationship has a positive correlation).

Answer:

0.6