Math Problem Statement

The table below gives the number of hours spent watching TV last week by a sample of 16 children. The values have been sorted. Find the minimum, maximum, range, mean, and standard deviation of the following data using StatCrunch, Excel, a calculator, or other technology. The minimum, maximum, range should be entered as exact values. Round the mean and standard deviation to two decimal places.

Solution

Here are the calculated values based on the dataHere are the calculated values based on the

  • Minimum = 13
  • Maximum = 47
  • Range = 34
  • Mean = 27.00
  • Standard Deviation = 9.73

Let me know if you would like more details or have any questions!

Here are five related questions:

  1. How do you calculate the median for this data set?
  2. What does the standard deviation tell us about the distribution of the data?
  3. How would the results change if we used a sample standard deviation instead of population standard deviation?
  4. Can the range alone provide insight into the spread of data?
  5. What impact would outliers have on the mean and standard deviation?

Tip: Standard deviation gives a sense of how spread out the data is from the mean, with a larger value indicating greater variability.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics

Formulas

Minimum = Smallest data value
Maximum = Largest data value
Range = Maximum - Minimum
Mean = (Sum of all data values) / (Number of data values)
Standard Deviation (Population) = sqrt((Σ (x - μ)^2) / N)

Theorems

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Suitable Grade Level

High School or College Level (Statistics)

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