Situation: You have 500 data points, which are normally distributed with a mean
ID: 3205972 • Letter: S
Question
Situation: You have 500 data points, which are normally distributed with a mean of 250 and a standard deviation of 25. 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.) When the new data point is added, what happens to the sample size (N)? When the new data point is added, what happens to the mean? When the new data point is added, what happens to the value of the mode? When the new' data point is added, what happens to the number of modes in the distribution? When the new data point is added, what happens to the range of the distribution? When the new data point is added, what happens to the value of the variance of the new distribution? When the new data point is added, what happens to the value of the skewness of the distribution? 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? What happens to the number of scores that are lower than 250? What happens to the number of scores that are higher than 250? What happens to the number of scores that are higher than 300? What happens to the number of scores that are more than 400?Explanation / Answer
a. Sample size(N) increases
b. Mean also increases with addition of this new oultier.
c. Mode will remain the same
d.Number of modes will also remain the same
e. Range of distribution will increase because of increase in Max value of distribution
f. Variance of new distribution will increase
g. Skewness will increase
i. Number of scores lower than 250 remain the same.
j. Number of scores higher than 250 increases
k. Number of scores higher than 300 increases
l. Number of scores higher than 400 increases