in a group there are 5 singers 3 dancers 2 artists 1 musician 1 guitarist and 1 teacher. the average height of the above mentioned people reduces by 2cm if i replace the guitarist with a joker. find the height of the joker if the height of the guitarist is 184 cm
Answers
Xi be the height of the i'th person. i = 1,2,3,4,5,6,7,8,9,10,11,12,13.
∑Xi = Summation of heights of all 13 people mentioned above.
The average height of the above mentioned people is denoted by x̅ .
x̅ = ∑Xi / n ( i takes values from 1 to 13)
x̅ = (X1 + X2 +....... + X12 + 184 ) / 13
x̅ = (∑Xi + 184) / 13 ( i takes values from 1 to 12)
13 * x̅ = ∑Xi + 184
- ∑Xi = 13 * x̅ - 184 equ (1) ( i take values from 1 to 12)
The average height of the above mentioned people x̅ reduces by 2cm if i replace the guitarist with a joker.
in simple words, x̅ reduces by 2 cm if we replace the guitarist with a joker.
x̅ -2 = (X1 + X2 +....... + X12 + Joker ) / 13
x̅ -2 = ( ∑Xi + Joker ) / 13 ( i take values from 1 to 12)
13*(x̅ -2 ) = ∑Xi + Joker
∑Xi = 13*(x̅ -2 ) - Joker
- ∑Xi = 13 * (x̅ - 2) - Joker equ (2) ( i take values from 1 to 12)
equating equations (1) and (2)
13 * x̅ - 184 = 13 * (x̅ - 2) - Joker
13 * x̅ - 184 = 13 * x̅ - 26 - Joker
Answer :- Joker = 158 Cm