To determine the relationship between the height of people and their shoe sizes, let's analyze the data shown in the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Height of People }( \text{cm} ) & \text{Shoe Size} \\
\hline
170 & 8.5 \\
172 & 9 \\
174 & 9.5 \\
176 & 10 \\
178 & 11 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Analysis:
1. Observation of Trends:
- As the height increases, the shoe size also increases.
2. Linear Relationship Check:
- We can look to see if the increase in height corresponds to a proportional increase in shoe size.
- Height increases are consistent: each step between heights is by 2 cm (170, 172, 174, 176, 178).
- Shoe size increases appear consistent too:
- From 8.5 to 9: an increase of 0.5
- From 9 to 9.5: an increase of 0.5
- From 9.5 to 10: an increase of 0.5
- From 10 to 11: an increase of 1
3. Correlation Estimation:
- Since both variables increase together and the pattern appears steady without any sudden dips or drops that would denote deviations, this points towards a consistent trend.
4. Conclusion:
- The relationship is positive, as both variables tend to increase together.
- It is linear, given the consistent incremental pattern observed.
- There are no deviations from this pattern in the table provided.
From the observations and analysis, the correct answer is:
A. positive linear association with no deviations
