1. Problem statement: Find the closest 3rd decile $D_3$ for the dataset: 50, 60, 55, 65, 70. 2. Formula and rules: The k-th decile $D_k$ corresponds to the $k\times10$th percentile. 3. A common position formula is $i=\frac{k(n+1)}{10}$, where $n$ is the sample size and $k=3$ for $D_3$. 4. Sort the data and identify $n$: Sorted data is 50, 55, 60, 65, 70, so $n=5$. 5. Compute the position $i$: $i=\frac{3(5+1)}{10}=\frac{18}{10}=1.8$. 6. Interpret the position: $i=1.8$ lies between the 1st value $x_1=50$ and the 2nd value $x_2=55$. 7. Interpolate linearly to get $D_3$: $D_3 = x_1 + (i-1)(x_2-x_1)$. 8. Substitute values: $D_3 = 50 + 0.8(55-50) = 50 + 0.8\times5 = 50 + 4 = 54$. 9. Compare with the provided options 62, 58, 55, 60 by computing absolute differences from $D_3=54$. 10. Differences: $|62-54|=8$, $|58-54|=4$, $|55-54|=1$, $|60-54|=6$. 11. Conclusion: The closest option to $D_3=54$ is 55. Final answer: 55.