Question

In: Statistics and Probability

The Accountability ratings for sixteen (16) school districts in the Delta Region of Mississippi on a...

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

Solutions

Expert Solution

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

=5th observation +0.1[6th-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

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

=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

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

=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

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

=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

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

=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

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

=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

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

=379+0.3[449-379]

=379+0.3(70)

=379+21

=400

D9= 400


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