You have 500 data points, which are normally distributed with a mean of 400 and

Question

You have 500 data points, which are normally distributed with a mean of 400 and a standard deviation of 50. All scores are integers. Then one new data point is added, which is far above the top end of the distribution. (Thus, the new data point has the very highest score in the distribution, by a considerable margin.)

________A. When the new data point is added, what happens to the sample size (N)?

________B. When the new data point is added, what happens to the value of the mean?

________C. When the new data point is added, what happens to the value of the mode?

________D. When the new data point is added, what happens to the number of modes in the distribution?

________E. When the new data point is added, what happens to the range of the distribution?

________F. When the new data point is added, what happens to the value of the variance of the new distribution?

________G. When the new data point is added, what happens to the value of the skewness of the distribution?

________H. What happens to the value of the z score of the new mean calculated using the 501 data points, compared to the value of the z score of the old mean calculated using the original 500 data points?

________I. What happens to the number of scores that are lower than 400?

________J. What happens to the number of scores that are higher than 400?

________K. What happens to the number of scores that are higher than 500?

________L. What happens to the number of scores that are higher than 700?

Explanation / Answer

A. When the new data point is added, what happens to the sample size (N) :it becomes 501

B)  When the new data point is added, what happens to the value of the mean : increases

C) When the new data point is added, what happens to the value of the mode :remain same 400

D) D. When the new data point is added, what happens to the number of modes in the : remain same 1

E) E. When the new data point is added, what happens to the range of the distribution : increases

F)

When the new data point is added, what happens to the value of the variance of the new distribution? -increases

G) When the new data point is added, what happens to the value of the skewness of the distribution :becme a little right skewed

H) What happens to the value of the z score of the new mean calculated using the 501 data points, compared to the value of the z score of the old mean calculated using the original 500 data points: decreases

I) What happens to the number of scores that are lower than 400: remains same

J)  What happens to the number of scores that are higher than 400 : increases by 1

K) What happens to the number of scores that are higher than 500 : : increases by 1

L )  What happens to the number of scores that are higher than 700: depends on numeric value of data point added

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