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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Statistics

NDA 2021 · Mathematics · Statistics

The marks obtained by 60 students in a certain subject out of 75...

The marks obtained by 60 students in a certain subject out of 75 are given below : <tableclass="qx−match−listqx−match−table"border="1"cellpadding="6"cellspacing="0"><tr><td>Marks</td><td>NumberofStudents</td></tr><tr><td>15−20</td><td>4</td></tr><tr><td>20−25</td><td>5</td></tr><tr><td>25−30</td><td>11</td></tr><tr><td>30−35</td><td>6</td></tr><tr><td>35−40</td><td>5</td></tr><tr><td>40−45</td><td>8</td></tr><tr><td>45−50</td><td>9</td></tr><tr><td>50−55</td><td>6</td></tr><tr><td>55−60</td><td>4</td></tr><tr><td>60−65</td><td>2</td></tr></table><table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>Marks</td><td>Number of Students</td></tr><tr><td>15-20</td><td>4</td></tr><tr><td>20-25</td><td>5</td></tr><tr><td>25-30</td><td>11</td></tr><tr><td>30-35</td><td>6</td></tr><tr><td>35-40</td><td>5</td></tr><tr><td>40-45</td><td>8</td></tr><tr><td>45-50</td><td>9</td></tr><tr><td>50-55</td><td>6</td></tr><tr><td>55-60</td><td>4</td></tr><tr><td>60-65</td><td>2</td></tr></table> What is the median?

Options

  1. A35
  2. B38
  3. C39
  4. D40

Correct answer

C. 39

Step-by-step solution

\begin{array}{|c|c|c|c|}\hline Marks & Midpoint & f & c f \hline 15-20 & 17.5 & 4 & 4 \hline 20-25 & 22.5 & 5 & 9 \hline 25-30 & 27.5 & 11 & 20 \hline 30-35 & 32.5 & 6 & 26 \hline 35-40 & 37.5 & 5 & 31 \hline 40-45 & 42.5 & 8 & 39 \hline 45-50 & 47.5 & 9 & 48 \hline 50-55 & 52.5 & 6 & 54 \hline 55-60 & 57.5 & 4 & 58 \hline 60-65 & 62.5 & 2 & 60 \hline\end{array} n=60- The classintervalcontainingnth 2orclass interval containing \frac{n^{\text{th }}}{2} or30^th itemis35−40.Therefore,{\text{th }} item is 35-40. Therefore,35-40is the medianclass.Weknowthatmedian class. We know that Median =l+n2−cf\timesh Here, l=35,n=60,f=5,h=5,c=26∴ Median =35+30−265×5M=39\begin{aligned}& \text{ Median }=l+\frac{\frac{n}{2}-c}{f} \timesh \\ & \text{ Here, }l=35, n=60, f=5, h=5, c=26 \\ & \therefore \text{ Median }=35+\frac{30-26}{5} \times5 \\ & \mathrm{M}=39 \end{aligned}$
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