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The shape of the normal curve depends on its ___________
- a)Mean deviation
- b)Standard deviation
- c)Quartile deviation
- d)Correlation
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The shape of the normal curve depends on its ___________a)Mean deviati...
This can be seen in the pdf of normal distribution where standard deviation is a variable.
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The shape of the normal curve depends on its ___________a)Mean deviati...
Standard Deviation
One of the key factors that determine the shape of the normal curve is the standard deviation. The normal curve is a symmetric bell-shaped curve, and the standard deviation helps to measure the spread of data points around the mean. Here's how the standard deviation affects the shape of the normal curve:
Spread of Data
- The standard deviation indicates how spread out the data points are in a dataset. A larger standard deviation means that the data points are spread out more widely, resulting in a flatter and wider curve.
- On the other hand, a smaller standard deviation means that the data points are clustered closely around the mean, leading to a taller and narrower curve.
Tails of the Curve
- The standard deviation also influences the tails of the normal curve. A larger standard deviation results in longer tails, indicating that there are more data points further away from the mean.
- Conversely, a smaller standard deviation leads to shorter tails, suggesting that the data points are concentrated closer to the mean.
Peak of the Curve
- The peak of the normal curve occurs at the mean, and the standard deviation affects the height of this peak. A larger standard deviation results in a lower peak, while a smaller standard deviation leads to a higher peak.
In conclusion, the standard deviation plays a crucial role in defining the shape of the normal curve by determining the spread, tails, and peak of the curve.
One of the key factors that determine the shape of the normal curve is the standard deviation. The normal curve is a symmetric bell-shaped curve, and the standard deviation helps to measure the spread of data points around the mean. Here's how the standard deviation affects the shape of the normal curve:
Spread of Data
- The standard deviation indicates how spread out the data points are in a dataset. A larger standard deviation means that the data points are spread out more widely, resulting in a flatter and wider curve.
- On the other hand, a smaller standard deviation means that the data points are clustered closely around the mean, leading to a taller and narrower curve.
Tails of the Curve
- The standard deviation also influences the tails of the normal curve. A larger standard deviation results in longer tails, indicating that there are more data points further away from the mean.
- Conversely, a smaller standard deviation leads to shorter tails, suggesting that the data points are concentrated closer to the mean.
Peak of the Curve
- The peak of the normal curve occurs at the mean, and the standard deviation affects the height of this peak. A larger standard deviation results in a lower peak, while a smaller standard deviation leads to a higher peak.
In conclusion, the standard deviation plays a crucial role in defining the shape of the normal curve by determining the spread, tails, and peak of the curve.
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The shape of the normal curve depends on its ___________a)Mean deviationb)Standard deviationc)Quartile deviationd)CorrelationCorrect answer is option 'B'. Can you explain this answer?
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The shape of the normal curve depends on its ___________a)Mean deviationb)Standard deviationc)Quartile deviationd)CorrelationCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The shape of the normal curve depends on its ___________a)Mean deviationb)Standard deviationc)Quartile deviationd)CorrelationCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The shape of the normal curve depends on its ___________a)Mean deviationb)Standard deviationc)Quartile deviationd)CorrelationCorrect answer is option 'B'. Can you explain this answer?.
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