Select the correct answer.
Which factor does the width of the peak of a normal curve depend on?
A. standard deviation
B. mean
C. median
D. mode
Answer (2)
The width of the peak of a normal curve depends on:
Standard deviation, which measures the spread of the data.
Mean, median, and mode represent the center of the distribution.
Standard deviation directly influences the width; larger values mean wider peaks.
Therefore, the correct answer is standard deviation: A
Explanation
Analyze the problem The question asks us to identify which factor determines the width of the peak of a normal distribution curve. Let's analyze the options provided.
Understanding Normal Distribution A normal distribution curve is a bell-shaped curve that is symmetric around the mean. The width of the curve indicates the spread of the data.
Role of Standard Deviation The standard deviation measures the spread or dispersion of the data around the mean. A larger standard deviation indicates a wider spread, while a smaller standard deviation indicates a narrower spread. Therefore, the standard deviation affects the width of the peak of the normal curve.
Role of Mean, Median, and Mode The mean , median , and mode are measures of central tendency. They indicate the center of the distribution but do not affect the spread or width of the peak. Changing the mean shifts the curve left or right but doesn't change its shape. In a perfectly symmetrical normal distribution, the mean, median, and mode are equal.
Conclusion Based on the above analysis, the width of the peak of a normal curve depends on the standard deviation.
Examples
Understanding the factors affecting a normal distribution is crucial in many real-world scenarios. For example, in quality control, the standard deviation of a product's measurements (like weight or size) determines the consistency of the production process. A smaller standard deviation means the products are more uniform. In finance, the standard deviation of stock returns indicates the volatility of the stock. A higher standard deviation suggests a riskier investment. In education, the standard deviation of test scores shows the variability in student performance. Knowing these concepts allows us to make informed decisions and predictions based on data.
The width of the peak of a normal curve is determined by the standard deviation, which measures the spread of data points around the mean. A larger standard deviation results in a wider peak, while a smaller one results in a narrower peak. Therefore, the correct answer is A: standard deviation.
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