Understand Z-Score Table & Outliers Impact on Mean

[F.B]

My textbook has the z-score table but it doesn't explain why the sign or magnitude means. It automatically assumes that we know.
I tried searching for this information but i can't find it.

1. Explain why do normal score tables typically not include z values greater than 2.99.

So can anyone give me the link to some sites that contain this type of information.

2. Explain why an outlier affects the mean more than the median or mode.

Is it because the mean changes with the data. If you change some of the values then the mean will also change but the mode and median should remain roughly the same.

 

[andrewchang]

an outlier affect the mean more because the value of it is taken into account as opposed to the median, where the position of it is simply taken into account (moving the median less than the mean would move)

 

[Architeuthis Dux]

1. Normal score tables typically do not include z values greater than 2.99 because they are considered to be extreme outliers. These values are so far from the mean that they have a very low probability of occurring in a normal distribution. Including these values in the table would not provide useful information, as they are already considered to be rare occurrences.

2. An outlier affects the mean more than the median or mode because the mean is calculated by taking the sum of all the values and dividing by the total number of values. This means that if there is an extreme value in the dataset, it will have a significant impact on the overall average. On the other hand, the median and mode only consider the middle or most frequent values in the dataset, respectively, and are not as affected by extreme values. Therefore, an outlier can skew the mean significantly, while the median and mode remain relatively unchanged.