Question

Sometimes we need to determine if data is actually “normal”. Determine if the data set includes more than 1 outlier.

85,53,70,10,11,40,10,65,55,25

1. What is my 5 number summary?

2. What is my interquartile range?

3. What is an outlier in my data set?

4. Do I have any outliers in the lower part of my data set?

Answer 1

Answer)

First we need to arrange the data in ascending order

10, 10, 11, 25, 40, 53, 55, 65, 70, 85

A)

Five number summary includes

Minimum, Q1, median, Q3, maximum

Minimum = 10

Q1= middlemost number of first half = 11

Median = middlemost number = 46.5 {in between 40 and 53}

Q3 = middlemost number of second half = 65

Maximum = 85

So, five number summary is

10, 11, 46.5, 65, 85

2)

Interquartile range is = Q3 - Q1 = 65 - 11 = 54

3)

Outlier is any thing below Q1 - (IQR*1.5) and anything above Q3 + (IQR*1.5)

11 - (54*1.5) = -70

65 + (54*1.5) = 146

Clearly there is no number below 70 or above 146

So there are no outlier

4)

No