1) one indicator of a outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80.
(a) if a data set has mean 70 and standard deviation 5, is 80 a suspect outlier? be sure to work that explains your answer
(b) if a data set ha mean 70 and standard deviation 3, is 80 a suspect outlier? be sure to explain the answer
Z = (score-mean)/SD
Insert the values to calculate Z.
To determine if 80 is a suspect outlier in both scenarios, we need to compare it with the mean and standard deviation of the given data sets.
(a) If a data set has a mean of 70 and a standard deviation of 5, we can use the formula:
Outlier threshold = Mean ± (2.5 * Standard Deviation)
In this case, the outlier threshold would be:
Outlier threshold = 70 ± (2.5 * 5) = 70 ± 12.5 = 57.5 and 82.5
Since 80 falls within the outlier threshold of 57.5 and 82.5, it is not a suspect outlier in this scenario.
(b) If a data set has a mean of 70 and a standard deviation of 3, the outlier threshold would be:
Outlier threshold = Mean ± (2.5 * Standard Deviation)
Outlier threshold = 70 ± (2.5 * 3) = 70 ± 7.5 = 62.5 and 77.5
In this case, 80 falls above the outlier threshold of 77.5. Thus, 80 is a suspect outlier in this scenario.