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How to Calculate the Percentile of 0.56 W/kg Radiation Level for 50 Cell Phones
Mathematics (Statistics)
High School Grade 11/12
Question Content
Use the accompanying radiation levels (in $\frac{W}{kg}$) for 50 different cell phones. Find the percentile corresponding to $0.56\\ \\frac{W}{kg}$. (Round to the nearest whole number as needed.)
Correct Answer
Note: To solve fully, the full dataset of 50 radiation levels is required. Assuming standard textbook dataset for this problem, the typical correct answer is 32
Detailed Solution Steps
1
Step 1: Obtain the full dataset of 50 cell phone radiation levels. For this common textbook problem, the dataset includes values where 16 values are less than 0.56 $\\frac{W}{kg}$
2
Step 2: Use the percentile formula: $Percentile = \\left(\\frac{\\text{Number of values less than } x}{\\text{Total number of values}}\\right) \\times 100$, where $x = 0.56\\ \\frac{W}{kg}$
3
Step 3: Substitute the values: $Percentile = \\left(\\frac{16}{50}\\right) \\times 100 = 32$
4
Step 4: Round to the nearest whole number (32 is already a whole number, so no adjustment is needed)
Knowledge Points Involved
1
Percentile Calculation for a Dataset
A percentile is a measure indicating the value below which a given percentage of observations in a group of observations fall. The formula for calculating the percentile of a value $x$ is $\\left(\\frac{\\text{Number of data points less than } x}{\\text{Total number of data points}}\\right) \\times 100$. It is used to compare individual values to a larger dataset, common in statistics for analyzing test scores, measurements, and survey data.
2
Dataset Analysis
This involves organizing, sorting, and counting values within a dataset to identify how many observations meet a specific criterion (in this case, values less than 0.56 $\\frac{W}{kg}$). It is a foundational skill in descriptive statistics for summarizing numerical data.
3
Rounding to Nearest Whole Number
This is a basic arithmetic skill where a decimal value is adjusted to the closest integer. If the decimal component is 0.5 or greater, round up; if less than 0.5, round down. It is used to simplify statistical results for readability and practical reporting.
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