Question

1. For each data set below, find the following: a) The 5 Number Summary; b) The IQR c) The “Outlier Fences”; d) List any outliers e) Sketch the box plot

45,70,71,73,75,80,81,85,100

Answer 1

Solution:
Given in the question
Data set is
45,70,71,73,75,80,81,85,100
So total no. of data values in data set = 9
Solution(a)
The 5 number summary can be calculated as
Minimum = 45
Q1 = (n+1)/4 = (9+1)/4 = 2.5th value i.e. 2nd and 3rd value is 70 and 71 so Q1= (70+71)/2 = 70.5
Median = (n+1)/2 = (9+1)/2 = 5th value i.e. 75
Q3 = 3*(9+1)/4 =7.5 th value i.e. 7th and 8th value are 81 and 85 so Q3 = (81+85)/2 = 83
Maximum = 100
So five number summary is 45, 70.5, 75, 83, 100
Solution(b)
Interquartile range = Q3 - Q1 = 83 - 70.5 = 12.5
Solution(c)
Outlier fences can be calculated as
Lower fence = Q1 - 1.5*IQR = 70.5 - 1.5*12.5 = 70.5 - 18.75 = 51.75
Upper fence = Q3 + 1.5*IQR = 83 + 15*12.5 = 83 + 18.75 = 101.75
Solution(d)
If any data value is lower than 51.75 or greater than 101.75 than this data value is outlier. So Data value 45 is outlier.
Solution(e)