Math Problem Statement

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

Solution

To find the 68th percentile (P68P_{68}) of this data set, follow these steps:

Step 1: Calculate the Locator (LL)

The locator LL for the percentile can be calculated using the formula:

L=k100×nL = \frac{k}{100} \times n

where:

  • k=68k = 68 (for the 68th percentile),
  • nn 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=90n = 90.

L=68100×90=0.68×90=61.2L = \frac{68}{100} \times 90 = 0.68 \times 90 = 61.2

So, the locator LL is 61.2.

Step 2: Use the Locator to Find P68P_{68}

Since L=61.2L = 61.2, we round up to the next whole number because LL 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, P68=62.9P_{68} = 62.9.

Summary:

  • Locator L=61.2L = 61.2,
  • 68th Percentile P68=62.9P_{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 LL 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.

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Math Problem Analysis

Mathematical Concepts

Percentiles
Descriptive Statistics

Formulas

L = (k / 100) * n

Theorems

Percentile Calculation Theorem

Suitable Grade Level

Grades 10-12