Let the random variable X represent the number of people living in a household in a certain town. The standard deviation of X
is 1.8. Which of the following statements is the best interpretation of the standard deviation?
A.The number of people living in a randomly selected household is expected to be 1.8 people.
B.The number of people living in a randomly selected household will be 1.8 people away from the mean.
C.On average, the number of people living in a household varies from the mean by about 1.8 people.
D.For a random sample of households, the average number of people per household is expected to be 1.8 people.
E. For a random sample of households, the average number of people per household will be 1.8 people away from the mean.
C?
Standard deviation is the expected margin from the mean (regardless if positive or negative), so that means the number of people living in a household would typically vary by 1.8 people.
So whatβs the answer?
The correct interpretation of the standard deviation in this case is option E: "For a random sample of households, the average number of people per household will be 1.8 people away from the mean."
Standard deviation is a measure of the dispersion or variability of the data points from the mean. In this context, the standard deviation tells us how much the number of people in each household deviates from the mean number of people per household. A standard deviation of 1.8 means that, on average, each household's number of people will be about 1.8 persons away from the mean.
Option A is incorrect because standard deviation does not represent an expected value or mean value. Option B is incorrect because it implies that every randomly selected household will have exactly 1.8 more or fewer people than the mean. Option C incorrectly states that the number of people varies by 1.8 people from the mean on average, rather than the individual households. Option D is incorrect because it states that the average number of people per household is expected to be 1.8, while the standard deviation measures the dispersion around the mean, not the mean itself.