15

15

Q1.

Solution

Q2.

Solution

Class interval x f xf d=|x-mean| fd 0-10 5 5 25 22 110 10-20 15 8 120 12 96 20-30 25 15 375 2 30 30-40 35 16 560 8 128 40-50 45 6 270 18 108 total 50 1350 472

M e a n equals fraction numerator begin display style stack sum f subscript i x subscript i with i below end style over denominator begin display style sum for i of end style f subscript i end fraction equals 1350 over 50 equals 27 M e a n space D e v i a t i o n equals fraction numerator 1 over denominator sum for i of f subscript i end fraction stack sum f subscript i d subscript i with i below equals 472 over 50 equals 9.44

Class interval x f cf d=|x-median| fd 0-10 5 5 5 20 100 10-20 15 8 13 5 40 20-30 25 15 28 0 0 30-40 35 16 44 10 160 40-50 45 6 50 20 120 total 50 420

N equals 50 rightwards double arrow N over 2 equals 25 T h e space c u m u l a t i v e space f r e q u e n c y space g r e a t e r space t h a n space 25 space i s space 28 space a n d space c o r r e s p o n d i n g space x space i s space 25 s o space m e d i a n space i s space 25. M e a n space d e v i a t i o n equals fraction numerator begin display style stack sum f subscript i d subscript i with i below end style over denominator begin display style stack sum f subscript i with i below end style end fraction equals 420 over 50 equals 8.4

Q3.

Solution

Q4.

Solution

Q5.

Solution

Q6.

Solution

Q7.

Solution

Firm B shows greater variability.

Q8.

Solution

Q9.

Solution

Q10.

Solution

Q11.

Solution

Q12.

Solution

n equals 15 comma space sigma squared equals 4 e a c h space o b s e r v a t i o n space i s space i n c r e a s e d space b y space 9 space t h e n space n e w space m e a n space w i l l space b e X with bar on top equals 1 over 15 space sum from i equals 1 to 15 of left parenthesis x subscript i plus 9 right parenthesis E left square bracket left parenthesis x plus 9 right parenthesis squared right square bracket equals 1 over 15 space sum from i equals 1 to 15 of left parenthesis x subscript i plus 9 right parenthesis squared equals 1 over 15 space sum from i equals 1 to 15 of left parenthesis x subscript i squared plus 81 plus 18 x subscript i right parenthesis n e w space v a r i a n c e equals E left square bracket left parenthesis x plus 9 right parenthesis squared right square bracket minus open parentheses X with bar on top close parentheses squared equals 1 over 15 space sum from i equals 1 to 15 of left parenthesis x subscript i squared plus 81 plus 18 x subscript i right parenthesis minus open parentheses 1 over 15 space sum from i equals 1 to 15 of left parenthesis x subscript i plus 9 right parenthesis close parentheses squared equals 1 over 15 space sum from i equals 1 to 15 of x subscript i squared plus 81 plus 18 over 15 space sum from i equals 1 to 15 of x subscript i minus open parentheses 1 over 15 space sum from i equals 1 to 15 of x subscript i close parentheses squared minus 81 minus 18 over 15 sum from i equals 1 to 15 of x subscript i equals 1 over 15 space sum from i equals 1 to 15 of x subscript i squared minus open parentheses 1 over 15 space sum from i equals 1 to 15 of x subscript i close parentheses squared equals sigma squared equals 4

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