The mode of the following frequency distribution is 46 and the total frequency is 150. Find the missing frequencies x and y.

The mode of the following frequency distribution is 46 and the total f

1.	The mode of the following frequency distribution is 46 and the total frequency is 150. Find the missing frequencies x and y.
Answer» Here, we are given total frequency is `150`. `6+8+17+x+42+30+y+8 = 150` `=> x+y+111 = 150` `=>x+y = 39` It means, both `x` and `y` does not exceed `42`. So, our modal class wil be `40-50`. Now, Mode can be given by formula, `Mode = l+(f_1-f_0)/(2f_1-f_0-f_2)h` Here, `l =` Lower limit of modal class `= 40` `f_1 = ` Frequency of Modal class `= 42` `f_2 = ` Frequency of Pre Modal class `= x` `f_3 = ` Frequency of Succeeding Modal class `= 30` `h =` Class interval `= 10` Putting these values in Mode formula, `Mode = 40+(42-x)/(84-30-x)10 = 40+(42-x)/(54-x)10` We are given, `Mode = 46` `=>40+(42-x)/(54-x)10 = 46` `=> (42-x)/(54-x)**10 = 6` `=> (42-x)/(54-x) = 6/10` `=> (42-x)/(54-x) = 3/5` `=>210-5x = 162-3x` `=>2x = 48` `=> x = 24` `=>y = 39-24 => y = 15`