Create a set of points that are very close together and then

Create a set of points that are very close together and then add a point that is far away from the set. What is the impact of the new point on the standard deviation?

Try to create a data set with at least 10 points that has a mean of approximately 5 and a standard deviation of approximately 1. Try to create another data set below the first with at least 10 points that has a mean of approximately 5 and a standard deviation of approximately 2. What did you do differently to create the data set with a larger standard deviation?

Solution

the new point that lies far away from the set is treated as an outlier. it has an impact on the standard deviation. it increases the standard deviation . as its deviation from the mean value is quite high. hence the standard deviation gets larger.

to create a data set with say 10 points that has mean approximately 5 and standard deviation approximately 1

simulation is used. 10 observations are simulated from N(5,1²) distribution.

these are

6.15531
5.31817
4.92798
5.00524
4.97559
4.67723
3.36751
4.68993

their mean is 5.07825 and standard deviation is 0.872290

now one more observation is added to the dataset that lies far from them. say 10.5450

so the new data set is
6.15531
5.31817
4.92798
5.00524
4.97559
4.67723
3.36751
4.68993

10.5450

based on 11 observations the mean is 5.57523   but the standard deviation is 1.84436. very close to 2.

so to create a data set with a larger standard deviation just one outlier is introduced to the existing dataset.