Genetic Variation
LESSON 10
Analyzing Data About Traits
A statistician collects the following height data in inches for a school district. The statistician says that it is a normal distribution. How did they draw this conclusion?
(1 point)
• The frequencies for each height range are different.
• When graphed, the data creates a bell curve
• The frequencies for the first and last height range are the same.
• When graphed, the data creates a straight line
The correct answer is: When graphed, the data creates a bell curve.
A normal distribution, also known as a bell curve, is characterized by the shape of the data when graphed. In a normal distribution, the frequencies of data points are highest at the center and gradually decrease as you move towards the extreme values. The shape of the distribution resembles a symmetrical bell shape, hence the term "bell curve." Therefore, if the data when graphed creates a bell curve pattern, it indicates a normal distribution.
The statistician drew the conclusion that the height data follows a normal distribution because when graphed, the data creates a bell curve.
To determine if the height data collected in the school district follows a normal distribution, the statistician likely used two key indicators: the frequencies of each height range and the shape of the graphed data.
1. The frequencies for each height range: A normal distribution is characterized by a specific pattern of frequencies for different values or ranges of the variable being studied. In this case, the statistician likely observed the frequencies for each height range and noticed that they were different. In a normal distribution, the frequencies usually decrease symmetrically as you move away from the center of the distribution.
2. The shape of the graphed data: Another important characteristic of a normal distribution is that when the data points are graphed, they tend to form a bell-shaped curve. This means that the majority of the data points cluster around the mean, with relatively fewer data points on either extreme. A bell curve is characterized by a smooth, symmetric shape that rises to a peak and then descends symmetrically.
Based on these factors, if the statistician observed that the frequencies for each height range were different and the graphed data formed a bell curve, they could conclude that the height data follows a normal distribution.