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If for some x $$ \in $$ R, the frequency distribution of the marks obtained by 20 students in a test is : .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg .tg-s6z2{text-align:center} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-hgcj{font-weight:bold;text-align:center} Marks 2 3 5 7 Frequency (x + 1)2 2x - 5 x2 - 3x x then the mean of the marks is

JEE · Math · previous-year question

  1. A.3.0
  2. B.2.8correct
  3. C.2.5
  4. D.3.2

Answer

B. 2.8

Explanation

Number of students $$ \Rightarrow {\left( {x + 1} \right)^2} + (2x - 5) + \left( {{x^2} - 3x} \right) + x = 20$$ $$ \Rightarrow 2{x^2} + 2x - 4 = 20$$ $$ \Rightarrow {x^2} + x - 12 = 0$$ $$ \Rightarrow (x + 4)(x - 3) = 0$$ $$x = 3$$ .tg {border-collapse:collapse;border-spacing:0;width:100%} .tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-yla0{font-weight:bold;text-align:left;vertical-align:middle} .tg .tg-nrix{text-align:center;vertical-align:middle} Marks 2 3 5 7 No. of students 16 1 0 3 Average marks = $${{32 + 3 + 21} \over {20}} = {{56} \over {20}} = 2.8$$

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