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 18 people away from the mean.

Question

Mathematics

Alfonso Garcia

1 November, 17:59

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 18 people away from the mean.

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Answers (1)

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Jakayla Avery · Answer 1

C) On average, the number of people living in a household varies from the mean by about 1.8 people

Step-by-step explanation:

Standard Deviation is a statistical measure of magnitude of variation / dispersion, of a set of values from the mean of the set.

Low standard deviation implies values are closer to the mean. High standard deviation implies values are far / wide spread around the mean.

If X represents number of people living in a household in a certain town; standard deviation reflects average level of variation around the mean people living in a household's town.

So, standard deviation = 1.8 implies : On average, the number of people living in a household varies from the mean by about 1.8 people.