Let's solve the problem step by step.

Step 1: Find the Locator $L$

The locator for the 37th percentile is given by the formula:

$L = \frac{P}{100} \times n$

where:

• $P = 37$ (percentile)
• $n = 117$ (total number of values)

$L = \frac{37}{100} \times 117$

$L = 43.29$

Since $L = 43.29$, this means we look for the 43rd value (rounding up if needed) in the sorted dataset.

Step 2: Find $P_{37}$

From the given dataset, we count to the 43rd value.

Counting through the dataset, the 43rd value is 45.2.

Thus, the 37th percentile value is:

$P_{37} = 45.2$

Final Answers:

• Locator $L$ = 43.29
• 37th Percentile $P_{37} = 45.2$

Would you like a further breakdown or explanation? Here are some related questions to expand on this topic:

1. How do we interpret the 37th percentile in a dataset?
2. What happens if $L$ is a whole number instead of a decimal?
3. How can we calculate the median using percentiles?
4. How do percentiles differ from quartiles?
5. How can we visualize percentiles on a histogram?

Tip: When dealing with percentiles, always round up $L$ if it's a decimal to ensure you're picking the correct value from the dataset.