https://file.aiquickdraw.com/mathbot/file/1728354422398f3tx8asi.jpg

To find the 68th percentile (\( P_{68} \)) of this data set, follow these steps:

### Step 1: Calculate the Locator (\( L \))
The locator \( L \) for the percentile can be calculated using the formula:

\[
L = \frac{k}{100} \times n
\]

where:
- \( k = 68 \) (for the 68th percentile),
- \( n \) is the total number of data points.

From the image, I can see that the dataset contains 90 numbers (9 rows and 10 columns). Thus, \( n = 90 \).

\[
L = \frac{68}{100} \times 90 = 0.68 \times 90 = 61.2
\]

So, the locator \( L \) is 61.2.

### Step 2: Use the Locator to Find \( P_{68} \)
Since \( L = 61.2 \), we round up to the next whole number because \( L \) is not an integer. Therefore, the 62nd value in the sorted dataset corresponds to the 68th percentile.

From the data, the 62nd value is **62.9**.

Thus, \( P_{68} = 62.9 \).

### Summary:
- Locator \( L = 61.2 \),
- 68th Percentile \( P_{68} = 62.9 \).

Would you like further details or have any other questions?

Here are 5 related questions to consider:
1. How do we calculate other percentiles using the same method?
2. What if the locator \( L \) had been a whole number?
3. Why do we use the next number when the locator isn't an integer?
4. How do percentiles differ from quartiles and deciles?
5. How can the histogram be used to estimate percentiles visually?

**Tip**: Always make sure the dataset is sorted before calculating percentiles.

To find P68, what is the value of the locator?

Learn how to calculate the 68th percentile of a sorted data set. Using descriptive statistics, the locator formula helps find the position of the percentile within a data set of 90 numbers. This problem is ideal for high school students studying percentiles.

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