Math Problem Statement
Solution
To find the 68th percentile () of this data set, follow these steps:
Step 1: Calculate the Locator ()
The locator for the percentile can be calculated using the formula:
where:
- (for the 68th percentile),
- 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, .
So, the locator is 61.2.
Step 2: Use the Locator to Find
Since , we round up to the next whole number because 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, .
Summary:
- Locator ,
- 68th Percentile .
Would you like further details or have any other questions?
Here are 5 related questions to consider:
- How do we calculate other percentiles using the same method?
- What if the locator had been a whole number?
- Why do we use the next number when the locator isn't an integer?
- How do percentiles differ from quartiles and deciles?
- 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