Question

What is the 5 number summary of the following data set?
11,2,3,5,8,9,8,11,78,12,14,2,3,6,5,11

Answer 1

we have,

11, 2, 3, 5, 8, 9, 8, 11, 78, 12, 14, 2, 3, 6, 5, 11

we can re arrange the data set as :

2, 2, 3, 3, 5, 5, 6, 8, 8, 9, 11, 11, 11, 12, 14, 78

we have a minimum value = 2

we have a maximum value = 78

As we have a data set which is even in quantity we can say that,

In a lower half we have a data set given by,

2, 2, 3, 3, 5, 5, 6, 8

we know that quartile Q₁ is nothing but a median of lower half which is given by,

In a upper half we have a data set given by,

8, 9, 11, 11, 11, 12, 14, 78

we know that quartile Q₃ is nothing but a median of upper half which is given by,

we can write five number summary as,

minimum = 2

Quartile Q₁ = 4

median = 8

Quartile Q₃ = 11

maximum = 78