Question

SAT scores for sixteen students are below. The results are below.

Use your calculator to find the Interquartile Range (IQR) for this sample.  

1059	1328	1175	1123	923	1017	1214	1042
1226	965	841	1053	1056	1393	1312	1222

Answer 1

Solution:
Arranging Observations in the ascending order, We get :
0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,5,5,5,5,5,6,6,6,7,7,8,8,9,9,9,9

Here, n=60

P75=(75(n+1)100)th value of the observation

=(75⋅61100)th value of the observation

=(45.75)th value of the observation

=45th observation +0.75[46th-45th]

=5+0.75[5-5]

=5+0.75(0)

=5+0

=5

P25=(25(n+1)100)th value of the observation

=(25⋅61100)th value of the observation

=(15.25)th value of the observation

=15th observation +0.25[16th-15th]

=1+0.25[1-1]

=1+0.25(0)

=1+0

=1

Interquartile Range = Q1 - Q3

= 5 - 1

= 4

Interquartile Range = 4