Question

The Accountability ratings for sixteen (16) school districts in the Delta Region of Mississippi on a 500 point rating scale are as follows: 302, 125, 225, 279, 108, 420, 350, 149, 129, 382, 114, 141, 180, 209, 156, & 163

Determine the following:

a. Third Decile

b. Fourth Decile

c. Fifth Decile

d. Sixth Dealle

e. Seventh Decile

f. Eighth Decile

g. Ninth Decile

***Please explain

Answer 1

Solution:
Arranging Observations in the ascending order, We get :
108,114,125,129,141,149,156,163,180,209,225,279,302,350,382,420

Here, n=16

a ) D₃=(3(n+1)10)^th value of the observation

=(3⋅17 /10)^th value of the observation

=(5.01)^th value of the observation

=5^th observation +0.1[6^th-5^th]

=141+0.1[149-141]

=141+0.1(8)

=141+0.8

=141.8

D₃=141.8

b ) D₄=(4(n+1)10)^th value of the observation

=(4⋅17 /10)^th value of the observation

=(6.8)^th value of the observation

=6^th observation +0.8[7^th-6^th]

=149+0.8[156-149]

=149+0.8(7)

=149+5.6

=154.6

D₄=154.6

c ) D₅=(5(n+1)10)^th value of the observation

=(5⋅17 /10)^th value of the observation

=(8.5)^th value of the observation

=8^th observation +0.5[9^th-8^th]

=163+0.5[180-163]

=163+0.5(17)

=163+8.5

=171.5

D₅= 171.5

d ) D₆=(6(n+1)10)^th value of the observation

=(6⋅17 /10)^th value of the observation

=(10.2)^th value of the observation

=10^th observation +0.2[11^th-10^th]

=209+0.2[225-209]

=209+0.2(16)

=209+3.2

=212.2

D₆= 212.2

e ) D₇=(7(n+1)10)^th value of the observation

=(7⋅17 /10)^th value of the observation

=(11.9)t^h value of the observation

=11^th observation +0.9[12^th-11^th]

=225+0.9[279-225]

=225+0.9(54)

=225+48.6

=273.6

D₇= 273.6

f ) D₈=(8(n+1)10)^th value of the observation

=(8⋅17 /10)^th value of the observation
=(13.6)^th value of the observation

=13th observation +0.6[14^th-13^th]

=302+0.6[350-302]

=302+0.6(48)

=302+28.8

=330.8

D₈= 330.8

g )D₉=(9(n+1)10)^th value of the observation

=(9⋅17 /10)^th value of the observation

=(15.3)^th value of the observation

=15^th observation +0.3[16^th-15^th]

=382+0.3[420-382]

=382+0.3(38)

=382+11.4

=393.4

D₉=393.4