ICSE Class 10 Answered

If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are the observations arranged in ascending order with median 24, find the value of x.

Asked by Topperlearning User | 07 Nov, 2017, 01:00: PM

Expert Answer

$Numbers space in space ascending space order space are 10 comma space 13 comma space 15 comma space 18 comma space straight x space plus space 1 comma space straight x space plus space 3 comma space 30 comma space 32 comma space 35 comma space 41 Here comma space straight n equals 10 space left parenthesis even right parenthesis therefore space Median equals fraction numerator open parentheses begin display style straight n over 2 end style close parentheses to the power of th space term plus open parentheses begin display style straight n over 2 plus 1 end style close parentheses to the power of th space term over denominator 2 end fraction rightwards double arrow 24 equals fraction numerator open parentheses begin display style 10 over 2 end style close parentheses to the power of th space term plus open parentheses begin display style 10 over 2 plus 1 end style close parentheses to the power of th space term over denominator 2 end fraction rightwards double arrow 24 equals fraction numerator 5 to the power of th space term plus 6 to the power of th space term over denominator 2 end fraction rightwards double arrow 24 equals fraction numerator left parenthesis straight x plus 1 right parenthesis plus left parenthesis straight x plus 3 right parenthesis over denominator 2 end fraction rightwards double arrow 24 equals fraction numerator 2 straight x plus 4 over denominator 2 end fraction rightwards double arrow 24 equals straight x plus 2 rightwards double arrow straight x equals 22$