Final answer:
The differences in the center and spread of the elephant height distributions can be assessed by mean and standard deviation or by median and interquartile range, especially if the distribution is symmetrical. Mean describes the central tendency while standard deviation indicates how spread out the data is.
Step-by-step explanation:
When analyzing the dot plots for the heights of two types of elephants, we look at various measures of central tendency and measures of spread. If the distribution is symmetrical, which means it looks the same on both sides of the center, the mean, median, and mode would typically be the same value or very close to each other. The spread of the distribution can be described using various statistics such as the range, interquartile range (IQR), variance, and standard deviation.
The mean is the average of the data points, while the standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, whereas a high standard deviation indicates that the values are spread out over a wider range. The median is the middle value when the data points are arranged in order, and the interquartile range (IQR) measures the middle 50% of the data, which is the range between the first and third quartiles.
In a normal distribution, the mean and standard deviation are all that are needed to describe the distribution since it is symmetric. The probability of finding a value within a certain distance from the mean can be calculated using the standard deviation, with 68% of data within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations from the mean.