Questions: The picture below has 3 normal curves plotted on the same set of axes.
Compare the means of the 3 distributions.
Compare the standard deviations of the 3 distributions. Explain your reasoning.
The three distributions all have the same mean because each curve has the same center and the three distributions have the same standard deviation because the distance from each graph's mean to the transition point or inflection point is the same for each distribution.
The three distributions have different values for the mean because each curve has a different center; but, on the other hand, the three distributions have the same standard deviation because the distance from each graph's mean to the transition point or inflection point is the same for each distribution.
The three distributions have different values for the mean because each curve has a different center and the three distributions have different standard deviations because the distance from each graph's mean to the transition point or inflection point is different for each distribution.
The three distributions all have the same mean because each curve has the same center; but, on the other hand, the three distributions have different standard deviations because the distance from each graph's mean to the transition point or inflection point is different for each distribution.
Transcript text: The picture below has 3 normal curves plotted on the same set of axes.
Compare the means of the 3 distributions.
Compare the standard deviations of the 3 distributions. Explain your reasoning
The three distributions all have the same mean because each curve has the same center and the three distributions have the same standard deviation because the distance from each graph's mean to the transition point or inflection point is the same for each distribution.
The three distributions have different values for the mean because each curve has a different center; but, on the other hand, the three distributions have the same standard deviation because the distance from each graph's mean to the transition point or inflection point is the same for each distribution.
The three distributions have different values for the mean because each curve has a different center and the three distributions have different standard deviations because the distance from each graph's mean to the transition point or inflection point is different for each distribution.
The three distributions all have the same mean because each curve has the same center; but, on the other hand, the three distributions have different standard deviations because the distance from each graph's mean to the transition point or inflection point is different for each distribution.
Solution
Solution Steps
Step 1: Comparing the means of the distributions
The means of the distributions are different because the peaks of the curves are at different points along the horizontal axis.
Step 2: Comparing standard deviations of the distributions
The standard deviations of the distributions are different. The standard deviation is a measure of the spread or width of the data. A wider curve corresponds to a larger standard deviation. In the given plot, the curves have different widths, so their standard deviations are different.
Final Answer:
The three distributions have different means because the centers of the curves are different. The three distributions have different standard deviations because the widths of the curves are different. The last option best describes this.