Percentile Use the weights from Exercise 1 to find the percentile for 3647 mg.

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Step 1: Arrange the weights in ascending order. The weights provided are already sorted in ascending order: 3511, 3516, 3521, 3531, 3532, 3545, 3583, 3588, 3590, 3617, 3621, 3635, 3638, 3643, 3645, 3647, 3666, 3673, 3678, 3723.

Step 2: Identify the position of the value 3647 in the sorted list. Count the number of values less than or equal to 3647. In this case, 3647 is the 16th value in the list.

Step 3: Calculate the total number of data points in the list. There are 20 weights in total.

Step 4: Use the formula for percentile rank: \( P = \frac{(L + 0.5)}{N} \times 100 \), where \( L \) is the number of values less than the given value, \( N \) is the total number of values, and \( P \) is the percentile rank.

Step 5: Substitute \( L = 15 \) (since there are 15 values less than 3647), \( N = 20 \), and calculate the percentile rank using the formula. This will give the percentile for 3647 mg.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Percentile

A percentile is a statistical measure that indicates the value below which a given percentage of observations in a group falls. For example, the 50th percentile (median) is the value that separates the higher half from the lower half of the data set. In this context, finding the percentile for a specific weight, such as 3647 mg, involves determining how many weights in the dataset are less than or equal to 3647 mg.

Data Set

A data set is a collection of related values or observations, often organized in a structured format. In this case, the weights provided in the image represent a data set from which we can analyze the distribution of values. Understanding the data set is crucial for calculating percentiles, as it provides the context and range of values needed for comparison.

Cumulative Frequency

Cumulative frequency is the running total of frequencies in a data set, showing how many observations fall below a particular value. To find the percentile for 3647 mg, one would calculate the cumulative frequency up to that value, which helps in determining its position relative to the entire data set. This concept is essential for understanding how data accumulates and aids in percentile calculations.

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