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JEE Main 20249 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2024 · 9 April · Morning Shift · Mathematics · Statistics

The frequency distribution of the age of students in a class of 40...

The frequency distribution of the age of students in a class of 40 students is given below. <tableclass="qx−match−listqx−match−table"border="1"cellpadding="6"cellspacing="0"><tr><td>Age<table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>Age151617181920No of Students58512xy If the mean deviation about the median is 1.25, then 4x+5y4 x+5 y is equal to :

Options

  1. A46
  2. B43
  3. C44
  4. D47

Correct answer

C. 44

Step-by-step solution

\begin{aligned} & \mathrm{x}+\mathrm{y}=10 \ldots \ldots \ldots .(1) \\ & \text{Median }=18=\mathrm{M} \\ & \text{M.D. }=\frac{\sum \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{\sum \mathrm{f}_{\mathrm{i}}} \\ & 1.25=\frac{36+\mathrm{x}+2 \mathrm{y}}{40} \\ & \mathrm{x}+2 \mathrm{y}=14 \ldots \ldots \ldots .(2) \\ & \text{ by (1) & (2) } \\ & \mathrm{x}=6, \mathrm{y}=4 \\ & \Rightarrow 4 \mathrm{x}+5 \mathrm{y}=24+20=44\end{aligned}Age⁡(xi)f∣xi−M∣fi∣xi−M∣1553151682161751518120019x1x20y22y\begin{array}{|l|l|l|l|} \hline \operatorname{Age}\left(\mathrm{x}_{\mathrm{i}}\right) & \mathrm{f} & \left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right| & \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right| \\ \hline 15 & 5 & 3 & 15 \\ \hline 16 & 8 & 2 & 16 \\ \hline 17 & 5 & 1 & 5 \\ \hline 18 & 12 & 0 & 0 \\ \hline 19 & \mathrm{x} & 1 & \mathrm{x} \\ \hline 20 & \mathrm{y} & 2 & 2 \mathrm{y} \\ \hline \end{array}$
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