Textbook Question
Percentiles. In Exercises 17–20, use the following radiation levels (in W/kg) for 50 different cell phones. Find the percentile corresponding to the given radiation level.
1.47 W/kg
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3. Describing Data Numerically
Standard Deviation
2:57 minutesProblem 3.3.25
Textbook Question
In Exercises 21–28, use the same list of cell phone radiation levels given for Exercises 17–20. Find the indicated percentile or quartile.
P50
Verified step by step guidance1
Step 1: Understand the problem. The task is to find the 50th percentile (P50) of the given data set. The 50th percentile is also known as the median, which is the value that separates the lower half and upper half of the data when arranged in ascending order.
Step 2: Arrange the data in ascending order. From the image, the data is already sorted in ascending order, so no further arrangement is needed.
Step 3: Determine the position of the 50th percentile in the data set. Use the formula for the position: \( P_k = \frac{k}{100} \times (n+1) \), where \( k \) is the percentile (50 in this case) and \( n \) is the total number of data points. Count the total number of data points in the list.
Step 4: Calculate the position using the formula. Substitute \( k = 50 \) and \( n \) (the total number of data points) into the formula. If the position is an integer, the value at that position is the 50th percentile. If the position is not an integer, interpolate between the two closest values.
Step 5: Identify the value corresponding to the calculated position in the sorted data set. This value is the 50th percentile (P50).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentiles
A percentile is a measure used in statistics to indicate the value below which a given percentage of observations fall. For example, the 50th percentile (P50) is the median, meaning that 50% of the data points are below this value. Understanding percentiles helps in interpreting the distribution of data and comparing individual scores to a larger dataset.
Quartiles
Quartiles are specific percentiles that divide a dataset into four equal parts. The first quartile (Q1) represents the 25th percentile, the second quartile (Q2) is the median or 50th percentile, and the third quartile (Q3) is the 75th percentile. Quartiles are useful for understanding the spread and center of a dataset, as they provide insights into the distribution of values.
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Data Distribution
Data distribution refers to the way in which data points are spread or arranged across different values. It can be visualized using graphs like histograms or box plots, which help identify patterns such as skewness, central tendency, and variability. Understanding the distribution of data is crucial for accurately calculating percentiles and quartiles, as these measures depend on the arrangement of the data.
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