Math Problem Statement

Listed below are the measured radiation emissions (in W/kg) corresponding to cell phones: A, B, C, D, E, F, G, H, I, J, and K respectively. The media often present reports about the dangers of cell phone radiation as a cause of cancer. Cell phone radiation must be 1.6 W/kg or less. Find the a. mean, b. median, c. midrange, and d. mode for the data.

Solution

Let's break down the task to solve the given questions based on the radiation emissions dataLet's break down the task to solve the given questions based on the radiation emissions

Data:

1.08, 1.48, 0.23, 0.41, 1.01, 1.12, 1.42, 0.75, 1.51, 0.69, 0.28

(a) Find the mean:

The mean is already calculated as 0.907.

(b) Find the median:

To find the median, we need to arrange the data in ascending order: 0.23, 0.28, 0.41, 0.69, 0.75, 1.01, 1.08, 1.12, 1.42, 1.48, 1.51

Since there are 11 values (an odd number), the median is the 6th value in the ordered list:

  • Median = 1.01

Would you like details on this or have any further questions?

Here are 5 questions you could explore:

  1. What is the definition of midrange in a data set?
  2. How is the mode of a data set determined?
  3. What is the effect of outliers on the mean and median?
  4. Can we calculate the standard deviation for this data?
  5. How does the median compare to the mean in terms of data distribution?

Tip: The median is often a better measure of central tendency when data includes outliers, as it isn't as sensitive to extreme values as the mean is.

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Math Problem Analysis

Mathematical Concepts

Mean
Median
Mode
Midrange
Data Analysis

Formulas

Mean = (Sum of all values) / (Number of values)
Median = Middle value of an ordered data set
Mode = Most frequent value in the data set
Midrange = (Maximum value + Minimum value) / 2

Theorems

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Suitable Grade Level

Grades 9-12