Question

7. A sample dataset has a mound-shaped and symmetric distribution with mean of 57 and a standard deviation of 11. a. Calculate the z-score for the observation with value 65. b. Calculate the z-score for the observation with value 21. c. Are either of these observations outliers? Explain and illustrate your answer with a graph, d. What are some possible causes of outliers in a dataset?

Answer 1

z score= (obseration-mean)/standard deviation. z score means how many times stabdard deviations a data point away from the mean.

hence a. z score=(65-57)/11=8/11=0.72

b. z score= (21-57)/11=-36/11=-3.27

c. the obseravtion 21 is an outlier.

why? because a z score(abosolute value) of 3 or above means the probability of getting that value is less than 0.3%. 99.7% of the data is within the -3<z<3 range. hence we can say that the score 21 is an outlier.

or we can say that a 99.7% of the data is within 3 standard deviation of the mean. that means 99.7% of the data is within 57-11x3=24 and 57+33=90. hence 21 is an outlier.

0214 : 1359 : 3413 : 3413 : 1359 : 0214 - 21 -2 -20 -lo и 65 lо 20 % 99.72% 95.44% 68.26% 57 68.26% 95.44% 99.72%

in the graph we can see that probability of getting a value less than 24 is very less (represented by the red area) hence finding 21 is rarer than this hence 21 is an outlier.

4. reasons we find outliers;

1. if we record the data wrong.

2. if the observation is characteristically different from the other observations

3.inconsistent sampling.

4. the environment in which the observation is made is different from other observations.