Subjective Questions
Q1:
Calculate the first quartile.
2, 18, 20, 14, 10, 4, 16
Type: Very_short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Now,<br>Arranging in ascerding order<br>2, 4, 10, 14, 16, 18, 20<br>Total number(N) = 7<br>We know that,<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{n + 1}{4} \end{pmatrix}\)<sup>th</sup> term<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{7 + 1}{4} \end{pmatrix}\)<sup>th</sup> term<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{8}{4} \end{pmatrix}\)<sup>th</sup> term<br>or, Q<sub>1</sub> = 2<sup>th</sup> term<br>\(\therefore\) The value of Q<sub>1</sub>is 4.</p>
Q2:
Calculate the third quartile.
90, 42, 52, 82, 72, 62, 100
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Now,<br>Arranging in ascending order<br>42, 52, 62, 72, 82, 90, 100 <br>Total number (N) = 7<br>We know that,<br>or, Q<sub>3</sub> = 3\(\begin{pmatrix}\frac{n + 1}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>3</sub> = 3\(\begin{pmatrix}\frac{7 + 1}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>3</sub> = 3\(\begin{pmatrix}\frac{8}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>3</sub> = 3 \(\times\) 2<sup>th</sup>item<br>or, Q<sub>3</sub> = 6<sup>th</sup>item<br>\(\therefore\) The value of Q<sub>3</sub>is 90.<br><br><br><br><br><br><br><br></p>
Q3:
Find the Q1, Q2 and Q3 from the following data.
72, 52, 50, 61, 56, 68, 64
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Now,<br>Arranging in ascending order<br>50, 52, 56, 61, 64, 68, 72<br>numbers = 7<br>We know that,<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{n + 1}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{7 + 1}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{8}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>1</sub> = 2<sup>th</sup>item<br>or,Q<sub>1</sub> = 52<br>Again,<br>or, Q<sub>2</sub>= \(\begin{pmatrix}\frac{n + 1}{2} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>2</sub>= \(\begin{pmatrix}\frac{7 + 1}{2} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>2</sub>= \(\begin{pmatrix}\frac{8}{2} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>2</sub>= 4<sup>th</sup>item<br>or, Q<sub>2</sub>= 61<br>Similarly,<br>or, Q<sub>3</sub>= 3\(\begin{pmatrix}\frac{n + 1}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>3</sub>= 3\(\begin{pmatrix}\frac{7 + 1}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>3</sub>= 3\(\begin{pmatrix}\frac{8}{4} \end{pmatrix}\)<sup>th</sup>item<br>or, Q<sub>3</sub>= 3 \(\times\)2<sup>th</sup>item<br>or, Q<sub>3</sub>= 6<sup>th</sup>item<br>or, Q<sub>3 </sub>= 68</p> <p>\(\therefore\) The value ofQ<sub>1</sub>, Q<sub>2</sub> and Q<sub>3</sub>is 52, 61 and 68 respectively.</p>
Q4:
Find the lower quartile and upper quartile of the following data set of scores:
18 20 23 20 23 27 24
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Arrange the values in ascending order of magnitude:</p> <p>18 20 20 23 23 23 24 27 29</p> <p>Here, n =7</p> <p>Lower quartile = value of\(\begin{pmatrix}\frac{n+1}{4} \end{pmatrix}\)<sup>th</sup>term</p> <p>= value of\(\begin{pmatrix}\frac{7+1}{4} \end{pmatrix}\)<sup>th</sup>term</p> <p>= value of\(\begin{pmatrix}\frac{8}{4} \end{pmatrix}\)<sup>th</sup>term</p> <p>= value of 2<sup><span style="font-size: xx-small;">nd</span></sup><span style="font-size: xx-small;"></span>item</p> <p>\(\therefore\) Lower Quartile = 20</p> <p>Upper Quartile = value of\(\begin{pmatrix}\frac{3(n+1)}{4} \end{pmatrix}\)<sup>th</sup>term</p> <p>= value of\(\begin{pmatrix}\frac{3(7+1)}{4} \end{pmatrix}\)<sup>th</sup>term</p> <p>= value of\(\begin{pmatrix}\frac{3 \times 8}{4} \end{pmatrix}\)<sup>th</sup>term</p> <p>= value of\(\begin{pmatrix}\frac{24}{4} \end{pmatrix}\)<sup>th</sup>term</p> <p>= value of 6<sup>th</sup>term</p> <p>\(\therefore\) Upper Quartile = 27</p>
Q5:
Compute Q1, Q2 and Q3 from the following data:
Marks |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
No. of Students |
2 |
4 |
6 |
12 |
8 |
6 |
1 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="305"><tbody><tr><td>Marks</td> <td>No. of students(f)</td> <td>cumulative frequency (c.f.)</td> </tr><tr><td>10</td> <td>2</td> <td>2</td> </tr><tr><td>20</td> <td>4</td> <td>6</td> </tr><tr><td>30</td> <td>6</td> <td>12</td> </tr><tr><td>40</td> <td>12</td> <td>24</td> </tr><tr><td>50</td> <td>8</td> <td>32</td> </tr><tr><td>60</td> <td>6</td> <td>38</td> </tr><tr><td>70</td> <td>1</td> <td>39</td> </tr><tr><td></td> <td>N = 39</td> <td></td> </tr></tbody></table><p>We have,</p> <p>Q1= value of \(\begin{pmatrix}\frac{n + 1}{4} \end{pmatrix}\)<sup>th</sup> term</p> <p>= value of \(\begin{pmatrix}\frac{39 + 1}{4} \end{pmatrix}\)<sup>th</sup> term</p> <p>= value of 10<sup>th</sup> term</p> <p>In c.f. column just greater than 10 is 12 and its coressponding value is 30.</p> <p>\(\therefore\) Q<sub>1</sub> = 30</p> <p>Q<sub>2 </sub>=value of \(\begin{pmatrix}\frac{n + 1}{2} \end{pmatrix}\)<sup>th</sup> term</p> <p>= value of \(\begin{pmatrix}\frac{39 + 1}{2} \end{pmatrix}\)<sup>th</sup> term</p> <p>= value of 20<sup>th</sup> term</p> <p>In c.f. column just greater than 20 is 24and its coressponding value is 40.</p> <p>\(\therefore\) Q<sub>2</sub>=40</p> <p>Q<sub>3 </sub>=value of \(\begin{pmatrix}\frac{3(n + 1)}{4} \end{pmatrix}\)<sup>th</sup> term</p> <p>=value of \(\begin{pmatrix}\frac{3(39 + 1)}{4} \end{pmatrix}\)<sup>th</sup> term</p> <p>=value of \(\begin{pmatrix}\frac{3 * 40}{4} \end{pmatrix}\)<sup>th</sup> term</p> <p>=value of \(\begin{pmatrix}\frac{3(39 + 1)}{4} \end{pmatrix}\)<sup>th</sup> term</p> <p>=value of 30<sup>th</sup> term</p> <p>In c.f. column just greater than 30 is 32 and its coressponding value is 50.</p> <p>\(\therefore\) Q<sub>3</sub>= 50</p>
Q6:
The number 6, x+5, 12, 14, 17, 20, 21 are in ascending order. If Q1 of this data is 8, find the value of x.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Here,<br>6, x+5, 12, 14, 17, 20, 21<br>Q<sub>1</sub>= 8<br>numbers = 7<br>We know that,<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{n + 1}{4} \end{pmatrix}\)<sup>th</sup> item<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{7 + 1}{4} \end{pmatrix}\)<sup>th</sup> item<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{8}{4} \end{pmatrix}\)<sup>th</sup> item<br>or, Q<sub>1</sub> = 2<sup>th</sup> item<br>or, Q<sub>1</sub> =x + 5<br>Now,<br>or,Q<sub>1</sub>= x + 5<br>or, 8= x + 5<br>or, x = 8 - 5<br>\(\therefore\) x = 5<br><br><br><br><br></p>
Q7:
Calculate Q1 and Q3 from the following data.
marks |
15 |
25 |
35 |
45 |
55 |
No. of students |
5 |
10 |
16 |
7 |
5 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="342"><tbody><tr><td>Marks</td> <td>Frequency (f)</td> <td>c.f</td> </tr><tr><td>15</td> <td>5</td> <td>5</td> </tr><tr><td>25</td> <td>10</td> <td>15</td> </tr><tr><td>35</td> <td>16</td> <td>31</td> </tr><tr><td>45</td> <td>7</td> <td>38</td> </tr><tr><td>55</td> <td>5</td> <td>43</td> </tr><tr><td></td> <td>N = 43</td> <td></td> </tr></tbody></table><p>Now,<br>or,Q<sub>1</sub>= \(\begin{pmatrix}\frac{N + 1}{4} \end{pmatrix}\)<sup>th</sup> item<br>or,Q<sub>1</sub>= \(\begin{pmatrix}\frac{43 + 1}{4} \end{pmatrix}\)<sup>th</sup> item<br>or,Q<sub>1</sub>= \(\begin{pmatrix}\frac{44}{4} \end{pmatrix}\)<sup>th</sup> item<br>or,Q<sub>1</sub>= 11<sup>th</sup> item</p> <p>In c.f column, c.f is just greater than 11 is 15 and its corresponding value is 25. So, Q<sub>1</sub> = 25<br>Again,<br>or, Q<sub>3</sub> = 3\(\begin{pmatrix}\frac{n + 1}{4} \end{pmatrix}\)<br>or, Q<sub>3</sub> = 3\(\begin{pmatrix}\frac{43 + 1}{4} \end{pmatrix}\)<br>or, Q<sub>3</sub> = 3\(\begin{pmatrix}\frac{44}{4} \end{pmatrix}\)<br>or, Q<sub>3</sub> = 3 \(\times\) 11<sup>th</sup>item<br>or, Q<sub>3</sub> = 33<sup>th</sup> item</p> <p>In c.f column, c.f is just greater than 33 is 38 and its corresponding value is 45.<br>So, Q<sub>3</sub> is 45.</p>
Q8:
Calculate the first quartile (lower quartile) from the given data.
Class |
0 -10 |
10 -20 |
20 - 30 |
30 - 40 |
40 - 50 |
frequency |
6 |
8 |
10 |
7 |
5 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="363"><tbody><tr><td>x</td> <td>f</td> <td>c.f</td> </tr><tr><td>0 -10</td> <td>6</td> <td>6</td> </tr><tr><td>10 - 20</td> <td>8</td> <td>14</td> </tr><tr><td>20 - 30</td> <td>10</td> <td>24</td> </tr><tr><td>30 - 40</td> <td>7</td> <td>31</td> </tr><tr><td>40 - 50</td> <td>5</td> <td>36</td> </tr><tr><td></td> <td>N = 36</td> <td></td> </tr></tbody></table><p>Now,<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{N}{4} \end{pmatrix}\)<sup>th</sup> item<br>or, Q<sub>1</sub> = \(\begin{pmatrix}\frac{36}{4} \end{pmatrix}\)<sup>th</sup> item<br>or, Q<sub>1</sub> = 9<sup>th</sup> item<br>In c.f column, c.f is just greater than 9 is 14 and its corresponding value is 10 - 20.<br>So, Q<sub>1</sub> lies in class 10 - 20<br>Then,<br>l = 10, c.f = 6, f = 8, and i = 10</p> <p>or, Q<sub>1</sub> =L + \(\frac{\frac{N}{4}-C.F}{f}\) × i<br>or,Q<sub>1</sub> = 10 + \(\frac{\frac{36}{4}-6}{8}\) × 10<br>or,Q<sub>1</sub> = 10 + \(\frac{9 - 6}{8}\) × 10<br>or,Q<sub>1</sub> = 10 + \(\frac{3}{8}\) × 10<br>or,Q<sub>1</sub> = 10 + \(\frac{3}{4}\) × 5<br>or,Q<sub>1</sub> = 10 + 0.75× 5<br>or,Q<sub>1</sub> = 10 +3.75<br>or,Q<sub>1</sub> = 13.75<br>\(\therefore\) The value of Q<sub>1</sub>is 13.75.<br><br></p>
Q9:
Calculate the first quartile and third quartile from the given data:
Class |
0-5 |
5-10 |
10-15 |
15-20 |
20-25 |
25-30 |
Frequency |
6 |
8 |
10 |
7 |
5 |
3 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="189"><tbody><tr><td>Class</td> <td>Frequency(f)</td> <td>c.f.</td> </tr><tr><td>0-5</td> <td>6</td> <td>6</td> </tr><tr><td>5-10</td> <td>8</td> <td>14</td> </tr><tr><td>10-15</td> <td>10</td> <td>24</td> </tr><tr><td>15-20</td> <td>7</td> <td>31</td> </tr><tr><td>20-25</td> <td>5</td> <td>36</td> </tr><tr><td>25-30</td> <td>4</td> <td>40</td> </tr><tr><td></td> <td>N =40</td> <td></td> </tr></tbody></table><p>Now,</p> <p>Q1 Class = value of (\(\frac{N}{4}\))<sup>th</sup> item</p> <p>= value of ( \(\frac{40}{4}\))<sup>th</sup> item</p> <p>= value of 10<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater than 10 is 14 and its corresponding class is (5-10).</p> <p>\(\therefore\) Q<sub>1</sub> lies in the class 5-10</p> <p>Here,</p> <p>\(\frac{N}{4}\) = 10,l= 5, c.f. = 6, f = 8 and i = 5</p> <p>\(\therefore\)Q<sub>1</sub>= l + \(\frac{\frac{N}{4}− c.f}{f}\) × i</p> <p>= 5 + \(\frac{10− 6}{8}\) ×5</p> <p>=5 + \(\frac{4}{8}\) ×5</p> <p>= 5 + 2.5</p> <p>= 7.5</p> <p>Again,</p> <p>Q<sub>3</sub> Class = value of(\(\frac{3N}{4}\))<sup>th</sup> item</p> <p>= value of(\(\frac{3 * 40}{4}\))<sup>th</sup> item</p> <p>=value of30<sup>th</sup> item</p> <p>In c.f. column, c.f.just greater than 30 is 31 and its corresponding class is 15-20.</p> <p>Here,</p> <p>\(\frac{3N}{4}\) = 30,l= 5, c.f. = 24, f = 7and i = 5</p> <p>\(\therefore\)Q<sub>3</sub>= l + \(\frac{\frac{3N}{4}− c.f}{f}\) × i</p> <p>= 5 + \(\frac{30− 24}{7}\) ×5</p> <p>= 5 + 4.28</p> <p>= 9.28</p> <p></p> <p></p>
Q10:
Calculate the third quartile (upper quartile) from the following data.
Class |
5 -10 |
10 -15 |
15 - 20 |
20 - 25 |
25 - 30 |
30 - 35 |
35 - 40 |
Frequency |
4 |
6 |
10 |
15 |
10 |
6 |
5 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="396"><tbody><tr><td>Class</td> <td>frequency</td> <td>c.f</td> </tr><tr><td>5 - 10</td> <td>4</td> <td>4</td> </tr><tr><td>10 - 15</td> <td>6</td> <td>10</td> </tr><tr><td>15 - 20</td> <td>10</td> <td>20</td> </tr><tr><td>20 - 25</td> <td>15</td> <td>35</td> </tr><tr><td>25 - 30</td> <td>10</td> <td>45</td> </tr><tr><td>30 - 35</td> <td>6</td> <td>51</td> </tr><tr><td>35 - 40</td> <td>5</td> <td>56</td> </tr><tr><td></td> <td>N = 56</td> <td></td> </tr></tbody></table><p>Now,<br>or, Q<sub>3</sub>= 3(\(\frac{N}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub>= 3(\(\frac{56}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub>= 3 \(\times\) 14<sup>th</sup> item<br>or, Q<sub>3</sub>= 42<sup>th</sup> item<br>In c.f column, c.f is just greater than 42 is 45 and its corresponding value is 25 - 30.<br>Now,<br>l = 25, c.f = 35, f = 10, and i = 5<br>Then,<br>or, Q<sub>3</sub>= L + \(\frac{\frac{3N}{4}-c.f}{f}\)× i<br>or, Q<sub>3</sub>= 25 + \(\frac{42 - 35}{10}\)× 5<br>or, Q<sub>3</sub>= 25 + \(\frac{7}{2}\)<br>or, Q<sub>3</sub>= 25 +3.5<br>or, Q<sub>3</sub>= 28.5<br>\(\therefore\) The value of Q<sub>3</sub> is 28.5.</p>
Q11:
The numbers 10, 20, 30, 40, 50, x + 25 and 70 are in ascerding order. If Q3 of this data is 60, find the value of x.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Here,<br>numbers = 7<br>Q<sub>3</sub>= 60<br>Now,<br>or, Q<sub>3</sub>= 3(\(\frac{N + 1}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub>= 3(\(\frac{7 + 1}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub>= 3(\(\frac{8}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub>= 3 \(\times\) 2<sup>th</sup> item<br>or, Q<sub>3</sub>= 6<sup>th</sup> item<br>i.e.Q<sub>3</sub>= x + 25<br>Then,<br>or,Q<sub>3</sub>= x + 25<br>or, 60 = x + 25<br>or, x + 60 - 25<br>\(\therefore\) x = 35<br><br><br><br></p>
Q12:
Calculate the first quartile (lower quartile) from the give data.
42, 58, 36, 38, 56, 50, 48
Type: Very_short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging in ascerding order<br>36, 38, 42, 48, 50, 56, 58<br>Total numbers (N) = 7<br>We know that,<br>or, Q<sub>1</sub>= (\(\frac{N+1}{4}\))<sup>th</sup> item<br>or, Q<sub>1</sub>= (\(\frac{7+1}{4}\))<sup>th</sup> item<br>or, Q<sub>1</sub>= (\(\frac{8}{4}\))<sup>th</sup> item<br>or, Q<sub>1</sub>= 2<sup>th</sup> item<br>i.e.Q<sub>1</sub>= 38</p>
Q13:
Calculate first, second and third quartile from the following data:
Marks |
30-40 |
40-50 |
50-60 |
60-70 |
70-80 |
80-90 |
Students |
5 |
12 |
25 |
15 |
8 |
3 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="189"><tbody><tr><td>Marks</td> <td>Students (f)</td> <td>c.f.</td> </tr><tr><td>30-40</td> <td>5</td> <td>5</td> </tr><tr><td>40-50</td> <td>12</td> <td>17</td> </tr><tr><td>50-60</td> <td>25</td> <td>42</td> </tr><tr><td>60-70</td> <td>15</td> <td>57</td> </tr><tr><td>70-80</td> <td>8</td> <td>65</td> </tr><tr><td>80-90</td> <td>3</td> <td>68</td> </tr><tr><td></td> <td>N =68</td> <td></td> </tr></tbody></table><p>Now,</p> <p>Q<sub>1</sub> Class = value of (\(\frac{N}{4}\))<sup>th</sup> item</p> <p>= value of ( \(\frac{68}{4}\))<sup>th</sup> item</p> <p>= value of 17<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater than 17 is 42 and its corresponding class is (50-60).</p> <p>\(\therefore\) Q<sub>1</sub> lies in the class 50-60</p> <p>Here,</p> <p>\(\frac{N}{4}\) = 17, l= 50, c.f. = 17, f = 25 and i =10</p> <p>\(\therefore\)Q<sub>1</sub>= l + \(\frac{\frac{N}{4}− c.f}{f}\) × i</p> <p>= 50 + \(\frac{17− 17}{25}\) ×10</p> <p>=50 + \(\frac{0}{25}\) ×10</p> <p>= 50 +0</p> <p>= 50</p> <p>Again,</p> <p>Q<sub>2</sub>Class = value of (\(\frac{N}{2}\))<sup>th</sup> item</p> <p>= value of ( \(\frac{68}{2}\))<sup>th</sup> item</p> <p>= value of 34<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater than 34 is 42 and its corresponding class is (50-60).</p> <p>\(\therefore\) Q<sub>2</sub>lies in the class 50-60</p> <p>Here,</p> <p>\(\frac{N}{2}\) = 34, l = 50, c.f. = 17, f = 25 and i =10</p> <p>\(\therefore\)Q<sub>1</sub>= l + \(\frac{\frac{N}{2}− c.f}{f}\) × i</p> <p>= 50 + \(\frac{34− 17}{25}\) ×10</p> <p>=50 + \(\frac{17}{25}\) ×10</p> <p>= 50 +6.8</p> <p>= 56.8</p> <p>Q<sub>3</sub> Class = value of(\(\frac{3N}{4}\))<sup>th</sup> item</p> <p>= value of(\(\frac{3 * 68}{4}\))<sup>th</sup> item</p> <p>=value of 51<sup>th</sup> item</p> <p>In c.f. column, c.f.just greater than 51 is 57 and its corresponding class is 60-70.</p> <p>Here,</p> <p>\(\frac{3N}{4}\) = 51, l= 60, c.f. = 42, f = 15 and i = 10</p> <p>\(\therefore\)Q<sub>3</sub>= l + \(\frac{\frac{3N}{4}− c.f}{f}\) × i</p> <p>= 60 + \(\frac{51− 42}{15}\) × 10</p> <p>= 60 + 6</p> <p>= 66</p> <p></p> <p></p>
Q14:
Find the third quartile (upper quartile) from the given data.
41, 82, 77, 52, 70, 62, 46
Type: Very_short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging in ascerding order<br>41, 46, 52, 62, 70, 77, 82<br>Total numbers (N)= 7<br>We know that,<br>or, Q<sub>3</sub> = 3(\(\frac{N+1}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub> = 3(\(\frac{7+1}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub> = 3(\(\frac{8}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub> = 3 \(\times\) 2<sup>th</sup> item<br>or, Q<sub>3</sub> = 6<sup>th</sup> item<br>i.e.Q<sub>3</sub> = 68</p>
Q15:
Find the Q1 and Q3 of the given data.
Weight (in kg) |
50 |
60 |
70 |
80 |
90 |
No. of teachers |
8 |
16 |
12 |
4 |
5 |
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="425"><tbody><tr><td>x</td> <td>f</td> <td>c.f</td> </tr><tr><td>50</td> <td>8</td> <td>8</td> </tr><tr><td>60</td> <td>16</td> <td>24</td> </tr><tr><td>70</td> <td>12</td> <td>36</td> </tr><tr><td>80</td> <td>4</td> <td>40</td> </tr><tr><td>90</td> <td>3</td> <td>43</td> </tr><tr><td></td> <td>N = 43</td> <td></td> </tr></tbody></table><p>Now,<br>or, Q<sub>1</sub> =(\(\frac{N+1}{4}\))<sup>th</sup> item<br>or, Q<sub>1</sub> =(\(\frac{43+1}{4}\))<sup>th</sup> item<br>or, Q<sub>1</sub> =(\(\frac{44}{4}\))<sup>th</sup> item<br>or, Q<sub>1</sub> =11<sup>th</sup> item<br>In c.f column, c.f is just greater than 11 is 24 and its corresponding value is 60.<br>So,Q<sub>1</sub> = 60<br>Again,<br>or, Q<sub>3</sub> =3(\(\frac{N+1}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub> =3(\(\frac{43+1}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub> =3(\(\frac{44}{4}\))<sup>th</sup> item<br>or, Q<sub>3</sub> =3 \(\times\) 11<sup>th</sup> item<br>or, Q<sub>3</sub> =33<sup>th</sup> item<br>In c.f column, c.f is just greater than 33 is 36 and its corresponding value is 70.<br>i.e.Q<sub>3</sub> = 70<br><br><br><br><br><br><br><br></p>