How to Calculate the Standard Deviation of the Numbers 1, 4, 5, 7, and 8
Step-by-step guide to calculate the standard deviation of 1, 4, 5, 7, and 8 with clear explanations and examples.
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To calculate the standard deviation of the numbers 1, 4, 5, 7, and 8: 1. Find the mean: (1+4+5+7+8)/5 = 5 2. Calculate each number's deviation from the mean: (-4, -1, 0, 2, 3) 3. Square these deviations: (16, 1, 0, 4, 9) 4. Find the average of these squared deviations: (16+1+0+4+9) / 5 = 6 5. Take the square root of this average: √6 ≈ 2.45
FAQs & Answers
- What is standard deviation in statistics? Standard deviation is a measure that quantifies the amount of variation or dispersion in a set of numerical data.
- How do you calculate the standard deviation of a data set? To calculate standard deviation, first find the mean, calculate each value's deviation from the mean, square these deviations, find their average, then take the square root of that average.
- Why is standard deviation important in data analysis? Standard deviation helps assess data variability, showing how spread out the values are from the mean, which is essential for statistical inference and decision-making.