Let X be the set of the 143 students in STAB57. This is a probability space when

Question

Let X be the set of the 143 students in STAB57. This is a probability space when given the uniform probability Let X- R be the random variable that asociates to each student their quiz 1 mark. Assume that the three (sample) quantiles for Px are respectively 3,6 and 8 What are the outliers? Assume now that we split up X into two groups X, and X2. giving a probability of Xi and in X2 to students in How do the quartiles and outliers change? . Are there any conditions under which the outliers do not change?

Explanation / Answer

given

Q1=3 Q2=6 Q3=8

so

IQR =Q3-Q1 =8-3=5

Now Outliers are given by

Q1-1.5IQR =3-1.5*5 =3-7.5=-4.5

Q3+1.5IQR =8+1.5*5 =8+7.5 =15.5

so values fall above the 15.5 are outliers as well as values fall below -4.5 are also outliers

when spiting the students in 2 parts X1 with prob =2/143 and X2 with prob 1/286

1. since on grouping the students there should be change in quartiles and outliers in each group its depends on marks of students in each group may decrease ,increase

2.for no change in outliers there should be same Q1 for each group as in 1st case also Q 3 shoulb be equal to previous Q3 value

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