Question

A college statistics class conducted a survey of how students spend their money. They asked 25 students to estimate how much money they typically spend each week on fast food. They determined that the mean amount spent on fast food is $31.52 with a standard deviation of $21.60. Later they realized that a value entered as $3 should have been $30. They recalculate the mean and standard deviation. The mean is now $32.60.

Which of the following is true about the standard deviation?i. The standard deviation will increase because we have increased the value of a data point.ii. The standard deviation will stay the same because the standard deviation is not affected by a change in a single measurement.iii. The standard deviation will decrease because this change moved a data point closer to the mean.

Answer 1

The standard deviation will decrease because this change moved a data point closer to the mean.

Explanation:

The value of $3, with a mean of $31.52 gives the following to standard deviation:

`(3-31.52)^(2)=813.39`

Whereas the value of $30 with a mean of $32.60 contributes:

`(30-32.60)^(2)=6.76`

As the observation is getting closer to the mean, it is reducing the size of the standard deviation.

Hence, the correct answer is : The standard deviation will decrease because this change moved a data point closer to the mean.