Math Problem Statement

Using your calculator, find the range and standard deviation, round to two decimal places: The table below gives the number of hours spent watching TV last week by a sample of 24 children.

Solution

I have opened the image you uploaded. The table shows the number of hours spent watching TV by 24 children. Let's extract the data and calculate the range and standard deviation as requested.

Here are the numbers from the table:

{26,39,57,74,44,77,69,25,38,41,54,48,50,53,42,56,47,49,58,52,46,60,67,57}\{26, 39, 57, 74, 44, 77, 69, 25, 38, 41, 54, 48, 50, 53, 42, 56, 47, 49, 58, 52, 46, 60, 67, 57\}

Steps to solve:

  1. Range: The range is already given as 78 (it seems to be calculated incorrectly, so I'll correct it).
  2. Standard Deviation: We'll calculate it based on the data provided.

Let me calculate both now.Here are the correct values based on the dataHere are the correct values based on the

  • Range: 5252 (not 78 as shown in the image)
  • Standard Deviation: 13.0613.06 (rounded to two decimal places)

Would you like further clarification on these calculations or more details?

Here are 5 related questions to expand your understanding:

  1. How is the range of a data set calculated?
  2. What is the difference between sample and population standard deviation?
  3. How do outliers affect the standard deviation?
  4. What is the significance of the standard deviation in statistics?
  5. Can you explain how the variance is related to the standard deviation?

Tip: Always ensure the data set size and type (sample vs. population) are considered when calculating standard deviation.

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Math Problem Analysis

Mathematical Concepts

Statistics
Range
Standard Deviation

Formulas

Range = Maximum value - Minimum value
Standard Deviation formula: \( \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (x_i - \bar{x})^2} \)

Theorems

Standard Deviation measures data dispersion

Suitable Grade Level

Grades 9-12