when a die is rolled 42 times it is so happened that a face having the digit i times occured 2i times. then find the mean deviation from the mean of this discrete frequency distribution. ans is ((80)/(63)) sol pls


Question and Answers Forum

All Questions Topic List
Probability and Statistics Questions
Previous in All Question Next in All Question
Previous in Probability and Statistics Next in Probability and Statistics
Question Number 151454 by gsk2684 last updated on 21/Aug/21

$w h e n a d i e i s r o l l e d 42 t i m e s i t i s s o$ $h a p p e n e d t h a t a f a c e h a v i n g t h e d i g i t i$ $t i m e s o c c u r e d 2 i t i m e s . t h e n f i n d t h e$ $m e a n d e v i a t i o n f r o m t h e m e a n o f t h i s$ $d i s c r e t e f r e q u e n c y d i s t r i b u t i o n .$ $a n s i s \frac{80}{63}$ $s o l p l s$
Commented by Olaf_Thorendsen last updated on 21/Aug/21
$• i = {1,2,3,4,5,6} • x_i = i • n_i = 2i • n = Σ_(i=1) ^6 n_i = 42 • f_i = (n_i /n) = ((2i)/(42)) = (i/(21)) • x^− = Σ_(i=1) ^6 f_i x_i = Σ_(i=1) ^6 (i^2 /(21)) = (((6×7×13)/6)/(21)) = ((13)/3) • σ = Σ_(i=1) ^6 f_i ∣x_i −x^− ∣ = Σ_(i=1) ^6 (i/(21))∣i−((13)/3)∣ = ((80)/(63))$
$∙ i = {1, 2, 3, 4, 5, 6}$ $∙ x_{i} = i$ $∙ n_{i} = 2 i$ $∙ n = \underset{i = 1}{\sum^{6}} n_{i} = 42$ $∙ f_{i} = \frac{n_{i}}{n} = \frac{2 i}{42} = \frac{i}{21}$ $∙ \bar{x} = \underset{i = 1}{\sum^{6}} f_{i} x_{i} = \underset{i = 1}{\sum^{6}} \frac{i^{2}}{21} = \frac{\frac{6 \times 7 \times 13}{6}}{21} = \frac{13}{3}$ $∙ σ = \underset{i = 1}{\sum^{6}} f_{i} ∣ x_{i} - \bar{x} ∣ = \underset{i = 1}{\sum^{6}} \frac{i}{21} ∣ i - \frac{13}{3} ∣ = \frac{80}{63}$
Commented by gsk2684 last updated on 21/Aug/21

$d h a n y a v a d h a m u l u (t h a n k s)$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum