Question

the average mark of candidates in an aptitude test was 128.5 with a standard deviation of 8.2 . three scores extracted from the test are 148,102,152. What is the average of the extracted scores that are extreme values. ​

Answer 1

Explanation:

Hello!

The variable of interest is

X: mark obtained in an aptitude test by a candidate.

This variable has a mean μ= 128.5 and standard deviation σ= 8.2

You have the data of three scores extracted from the pool of aptitude tests taken.

148, 102, 152

The average is calculated as X[bar]= Σx/n= (148+102+152)/3= 134

An outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.

Using the mean and the standard deviation, an outlier is any value that is three standard deviations away from the mean: μ±3σ

Using the population values you can calculate the limits that classify an observed value as outlier:

μ±3σ

128.5±3*8.2

(103.9; 153.1)

This means that any value below 103.9 and above 153.1 can be considered an outlier.

For this example, there is only one outlier, that this the extracted score 102

I hope this helps!