More and more universities are facing cutbacks in state fund

More and more universities are facing cutbacks in state funding.Asa result , there is considerable fund raising being done by alumni and specific college entities. A random sample of 16 finacial gifts given to a university is selected for 2008. The data ( in thousands of dollars) is shown below:

1.0, 3.0 , 5.7, 3.0 , 0.3 , 0.3 , 1.6, 8.8

1.0 , 0.8 , 0.5 , 2.4 , 2.4 , 4.5 , 3.6 , 3.2

1) Find the sample interquartile rang (IQR)?

2) Find the upper fence and lower fence for the dataset ?

3) Is the observation 8.8 an outlier. Use Z- score to answer this question?

Solution

More and more universities are facing cutbacks in state funding.Asa result , there is considerable fund raising being done by alumni and specific college entities. A random sample of 16 finacial gifts given to a university is selected for 2008. The data ( in thousands of dollars) is shown below:

1.0, 3.0 , 5.7, 3.0 , 0.3 , 0.3 , 1.6, 8.8

1.0 , 0.8 , 0.5 , 2.4 , 2.4 , 4.5 , 3.6 , 3.2

1) Find the sample interquartile rang (IQR)?

Q1= 0.95

Q3=3.30

IQR =3.30-0.95 =2.35

2) Find the upper fence and lower fence for the dataset ?

LF = Q1 - 1.5 * IQR = 0.95-1.5*2.35 =   -2.575
UF = Q3 + 1.5 * IQR = 3.30+1.5*2.35 =6.825

3) Is the observation 8.8 an outlier. Use Z- score to answer this question?

Mean=2.631, Sd=2.277

Z value for 8.8, z=(8.8 -2.631)/2.277   =2.709

There is no uniform value for finding outlier using z value

If you take cut off value 3, our value less than 3, it is not outlier

If you take cut off value 2 or 2.5 , our value is above this, it is an outlier