Question

The Accountability ratings for sixteen (16) school districts in the Delta Region of Mississippi on a 500 point rating scale are as follows: 102, 225, 222, 379, 208, 120, 250, 449, 229, 182, 214, 141, 150, 309, 256, & 263 Determine the following: a. Third Decile b. Fourth Decile c. Fifth Decile d. Sixth Decile e. Seventh Decile f. Eighth Decile g. Ninth Decile

Answer 1

Solution:
Arranging Observations in the ascending order, We get :
102,120,141,150,182,208,214,222,225,229,250,256,263,309,379,449

Here, n=16

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

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

=(5.1)^th value of the observation

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

=182+0.1[208-182]

=182+0.1(26)

=182+2.6

=184.6

D₃= 184.6

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

=(4⋅1710)^th value of the observation

=(6.8)^th value of the observation

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

=208+0.8[214-208]

=208+0.8(6)

=208+4.8

=212.8

D₄= 212.8

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]

=222+0.5[225-222]

=222+0.5(3)

=222+1.5

=223.5

D₅= 223.5

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]

=229+0.2[250-229]

=229+0.2(21)

=229+4.2

=233.2

D₆= 233.2

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

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

=(11.9)^th value of the observation

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

=250+0.9[256-250]

=250+0.9(6)

=250+5.4

=255.4

D₇=255.4

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

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

=263+0.6[309-263]

=263+0.6(46)

=263+27.6

=290.6

D₈= 290.6

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]

=379+0.3[449-379]

=379+0.3(70)

=379+21

=400

D₉= 400