MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
**Problem:** After doubling all of the scores, the mean was found to be 28 and the standard deviation was 4. What were the values for the mean and standard deviation (SD) before the change? Explain. **Solution:** To find the original mean and standard deviation before the scores were doubled, we can use the properties of mean and standard deviation with respect to scaling: 1. **Mean:** - If all scores are doubled, the mean of the scores is also doubled. - Thus, if the doubled mean is 28, the original mean (\(\mu\)) is: \[ \mu = \frac{28}{2} = 14 \] 2. **Standard Deviation:** - The standard deviation also scales linearly with multiplication. - If the doubled standard deviation is 4, the original standard deviation (\(\sigma\)) is: \[ \sigma = \frac{4}{2} = 2 \] Therefore, before doubling, the mean of the scores was 14 and the standard deviation was 2.
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Transcribed Image Text:**Problem:** After doubling all of the scores, the mean was found to be 28 and the standard deviation was 4. What were the values for the mean and standard deviation (SD) before the change? Explain. **Solution:** To find the original mean and standard deviation before the scores were doubled, we can use the properties of mean and standard deviation with respect to scaling: 1. **Mean:** - If all scores are doubled, the mean of the scores is also doubled. - Thus, if the doubled mean is 28, the original mean (\(\mu\)) is: \[ \mu = \frac{28}{2} = 14 \] 2. **Standard Deviation:** - The standard deviation also scales linearly with multiplication. - If the doubled standard deviation is 4, the original standard deviation (\(\sigma\)) is: \[ \sigma = \frac{4}{2} = 2 \] Therefore, before doubling, the mean of the scores was 14 and the standard deviation was 2.
Expert Solution
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Step 1: Given

Let's denote the original mean as  and the original standard deviation as .

After doubling all of the scores, the new mean () and new standard deviation (sigma apostrophe) were found to be 28 and 4, respectively.


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