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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 mode?

Options

  1. A27.27
  2. B27.73
  3. C27.93
  4. D28.27

Correct answer

B. 27.73

Step-by-step solution

The class interval for highest frequency is 25−3025-30. There fore, 25-30 is the mode class. We know that  Mode =l+fm−fm−1(fm−fm−1)+(fm−fm+1)×h\text{ Mode }=l+\frac{f_m-f_{m-1}}{\left(f_m-f_{m-1}\right)+\left(f_m-f_{m+1}\right)} \times h Here ,l=25,fm=11,fm−1=5,fm+1=6,h=5∴ Mode =25+11−5(11−5)+(11−6)×5Mode =27.727≅27.73\begin{aligned} & \text{ Here }, l=25, f_m=11, f_{m-1}=5, f_{m+1}=6, h=5 \\ & \therefore \text{ Mode }=25+\frac{11-5}{(11-5)+(11-6)} \times 5 \\ & \text{Mode }=27.727 \cong 27.73\end{aligned}$$
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