A random sample of dates taken from headstones at a cemetery in Pleasanton, California, showed an average lifespan of 70 years with a standard deviation of 20 years. Assuming the distribution is unimodal, which of the following is most likely a
good description of the distribution?
A. The distribution is most likely skewed to the left.
B. The distribution is most likely skewed to the right.
C. The distribution is most likely relatively symmetric.
D. We cannot tell the shape of the distribution from these
statistics.
Since since people over 70 are more likely to die, the mode is likely to be above the mean. In addition, there are relatively few people who die in childhood or adolescence, I would assume a likely distribution would be negatively skewed (to the left), A.
To determine the likely shape of the distribution, we can examine the given information.
The average lifespan of 70 years is a measure of central tendency, which indicates that the distribution is centered around this value. However, to determine if the distribution is skewed to the left or right, we need to consider the standard deviation.
The standard deviation of 20 years tells us about the spread or variability of the data points. If the standard deviation is relatively small, it suggests that the data points are tightly clustered around the average, resulting in a relatively symmetric distribution.
However, if the standard deviation is large, it indicates that the data points are more spread out from the average, and the distribution may be skewed.
In this case, the standard deviation of 20 years is not extremely large, suggesting that the distribution is likely relatively symmetric. Therefore, the most appropriate answer would be C. The distribution is most likely relatively symmetric.