Question

Consider the following ordered data. 8 11 11 12 13 13 14 15 16

(a) Find the

low,

Q1,

median,

Q3,

and high. (For each answer, enter a number.)

(b) Find the interquartile range. (Enter a number.)

Answer 1

For the given sample data 8 11 11 12 13 13 14 15 16

a) The five-point summary is shown below as:

Minimum: 8
Quartile Q1: Q1 is the median of the first half of the data set which is also the 25th percentile of the data set hence the middle value of the 1st half of the data set is between 2nd and 3rd position so, Q1=(11+11)/2=11
Median: Median is the Q2 Which is the middle value of the whole data set hence Median=13
Quartile Q3: Q3 is the Median of the 2nd half of the data set hence the middle value of the 2nd half of the data set lies between 8th and 9th position so, Q3=(14+15)/2=14.5
Maximum: 16

b) IQR= Interquartile range is calculated as Q3-Q1=14.5-11=3.5