Math Problem Statement

Given a random sample of five data, calculate the standard deviation and range. Round to one decimal place.

x 13 3 1 25 20

Standard deviation = Question HelpQuestion 1: Video1 Submit QuestionQuestion 1 UnattemptedQuestion 2 Check 0/1 ptRetries 3Reattempts 98 The table below gives the number of hours spent watching TV last week from a random sample of 24 children. Calculate the range.

25 70 63 55 85 66 21 28 87 75 84 21 45 47 65 35 37 32 50 46 40 41 93 19

Range =

Solution

For the first set of dataFor the first set of

  • The standard deviation is approximately 10.410.4.
  • The range is 2424.

Now, let's calculate the range for the second set of dataFor the first set of

  • The standard deviation is approximately 10.410.4.
  • The range is 2424.

Now, let's calculate the range for the second set of

The data is: 25,70,63,55,85,66,21,28,87,75,84,21,45,47,65,35,37,32,50,46,40,41,93,1925, 70, 63, 55, 85, 66, 21, 28, 87, 75, 84, 21, 45, 47, 65, 35, 37, 32, 50, 46, 40, 41, 93, 19

For the second set of data, the range is 7474.

Would you like further details on how these calculations were done or have any questions?

Here are some related questions you might find useful:

  1. How is the standard deviation calculated step-by-step?
  2. What is the difference between population standard deviation and sample standard deviation?
  3. How does range provide insights into data variability?
  4. What are other measures of dispersion besides range and standard deviation?
  5. How do outliers affect the standard deviation and range?

Tip: The range is highly sensitive to outliers, while the standard deviation provides a more comprehensive measure of data spread.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics

Formulas

Standard deviation formula: sqrt(Σ(xi - x̄)^2 / (n - 1))
Range formula: Max(data) - Min(data)

Theorems

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Suitable Grade Level

Grades 10-12

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