Questions: Calculate the mean (X̄) of the data. Round your answer to 2 decimal places as needed. Calculate the standard deviation ( S ) using your graphing calculator. Hint: Also verify that the mean you calculated in part d matches the mean from the calculator. Standard deviation =1.99 Round your answer to 2 decimal places as needed. Determine the range of variation: (X̄-S, X̄+S)=(1.45, 5.43) Round your answers to 2 decimal places as needed. Calculate what percent of the data values are within one standard deviation of the mean. Hint: Create a histogram on paper and shade the included region(s) on your histogram to help visualize the shaded area and help with calculations. Total area of shaded region = Round your answer to 2 decimal places as needed. Percent of area within one standard deviation = Round your answer to 2 decimal places as needed.

Calculate the mean (X̄) of the data. Round your answer to 2 decimal places as needed. Calculate the standard deviation ( S ) using your graphing calculator. Hint: Also verify that the mean you calculated in part d matches the mean from the calculator. Standard deviation =1.99 Round your answer to 2 decimal places as needed. Determine the range of variation: (X̄-S, X̄+S)=(1.45, 5.43) Round your answers to 2 decimal places as needed. Calculate what percent of the data values are within one standard deviation of the mean. Hint: Create a histogram on paper and shade the included region(s) on your histogram to help visualize the shaded area and help with calculations. Total area of shaded region = Round your answer to 2 decimal places as needed. Percent of area within one standard deviation = Round your answer to 2 decimal places as needed.
Transcript text: Calculate the mean $(\bar{X})$ of the data. Round your answer to 2 decimal places as needed. Calculate the standard deviation ( $S$ ) using your graphing calculator. Hint: Also verify that the mean you calculated in part d matches the mean from the calculator. Standard deviation $=1.99$ Round your answer to 2 decimal places as needed. Determine the range of variation: $(\bar{X}-S, \bar{X}+S)=(1.45, 5.43)$ Round your answers to 2 decimal places as needed. Calculate what percent of the data values are within one standard deviation of the mean. Hint: Create a histogram on paper and shade the included region(s) on your histogram to help visualize the shaded area and help with calculations. Total area of shaded region = $\square$ Round your answer to 2 decimal places as needed. Percent of area within one standard deviation $=$ $\square$ Round your answer to 2 decimal places as needed.
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Solution

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Solution Steps

Step 1: Calculate the Mean

The mean \( \bar{X} \) of the data is calculated as follows:

\[ \bar{X} = \frac{\sum_{i=1}^N x_i}{N} = \frac{40}{10} = 4.0 \]

Thus, the mean is:

\[ \bar{X} = 4.0 \]

Step 2: Calculate the Standard Deviation

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 0.0 \]

The standard deviation \( S \) is then:

\[ S = \sqrt{0.0} = 0.0 \]

Thus, the standard deviation is:

\[ S = 0.0 \]

Step 3: Determine the Range of Variation

The range of variation is calculated as:

\[ (\bar{X} - S, \bar{X} + S) = (4.0 - 0.0, 4.0 + 0.0) = (4.0, 4.0) \]

Final Answer

  • Mean \( \bar{X} = 4.0 \)
  • Standard Deviation \( S = 0.0 \)
  • Range of Variation \( (4.0, 4.0) \)

Thus, the final boxed answers are:

\[ \boxed{\bar{X} = 4.0} \] \[ \boxed{S = 0.0} \] \[ \boxed{(4.0, 4.0)} \]

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