there are four childeren in a family. the two oldest children are twins. the mean of the four children is 14.25, median is 15.5 and mode is 16. use this information to identify the age of four children

Asked by rajanghai.2014 | 22nd Aug, 2015, 05:10: PM

Expert Answer:

L e t space a comma b comma c comma d space b e space t h e space a g e s space o f space t h e i r space c h i l d r e n space i n space i n c r e a sin g space o r d e r. T h e r e f o r e comma space a less than b less than c less than d. G i v e n space t h a t space t w o space o l d e s t space c h i l d r e n space a r e space t w i n s. T h e r e f o r e comma space w e space h a v e comma space c equals d  G i v e n space t h a t space t h e space m e a n space o f space t h e i r space a g e s equals 14.5 rightwards double arrow fraction numerator a plus b plus c plus d over denominator 4 end fraction equals 14.5 rightwards double arrow a plus b plus c plus d equals 4 cross times 14.5 rightwards double arrow a plus b plus c plus d equals 57 rightwards double arrow a plus b plus 2 c equals 57 space space space space open square brackets because c equals d close square brackets rightwards double arrow a plus b equals 57 minus 2 c... left parenthesis 1 right parenthesis  A l s o space g i v e n space t h a t space m e d i a n space 15.5 T h e space a g e s space i n space i n c r e a sin g space o r d e r space a r e colon space a comma b comma c comma d T h u s comma space m e d i a n equals fraction numerator b plus c over denominator 2 end fraction S i n c e space m e d i a n space g i v e n space i s space 15.5 comma fraction numerator b plus c over denominator 2 end fraction equals 15.5 rightwards double arrow b plus c equals 2 cross times 15.5 rightwards double arrow b plus c equals 31 rightwards double arrow c equals 31 minus b S u b s t i t u t i n g space t h e space v a l u e space c equals 31 minus b comma space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma a plus b equals 57 minus 2 open parentheses 31 minus b close parentheses rightwards double arrow a plus b equals 57 minus 62 plus 2 b rightwards double arrow a minus b equals negative 5... left parenthesis 2 right parenthesis  G i v e n space t h a t space m o d e space o f space t h e space d a t a space i s space 16. S i n c e space t h e r e space i s space o n e space t w i n space p a i r space o f space c h i l d r e n comma space a g e s space o f space t w i n s equals 16 rightwards double arrow c equals d equals 16 S u b s t i t u t i n g space t h e space v a l u e space c equals 16 space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e a plus b equals 57 minus 2 cross times 16 rightwards double arrow a plus b equals 25... left parenthesis 3 right parenthesis a minus b equals negative 5... left parenthesis 2 right parenthesis S o l v i n g space e q u a t i o n s space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space a equals 10 space a n d space b equals equals 15 T h u s comma space t h e space a g e s space o f space c h i l d r e n space i n space t h e space h o u s e space a r e colon space 10 comma space 15 comma space 16 comma space 16

Answered by Vimala Ramamurthy | 23rd Aug, 2015, 09:20: AM