Subjective Questions
Q1:
Find the Quartiles of the list:
30, 35, 25, 16, 12, 8, 10.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>8, 10, 12, 16, 25, 30, 35.</p> <p>N=7</p> <p>Now, Position of Q<sub>1</sub>= (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{7+1}{4}\))<sup>th</sup> item.</p> <p>= 2<sup>th</sup> item.</p> <p>In given data 2<sup>th</sup> item is 10.</p> <p>Therefore, Q<sub>1</sub> =10.</p>
Q2:
Find the Quartile(Q1) of the list:
16, 10, 12, 18, 20, 14, 30, 28, 40.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging, the data in ascending order.</p> <p>10, 12, 16, 18, 20, 24, 28, 30, 40.</p> <p>N=9</p> <p>Now, Position of Q<sub>1</sub> = (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{9+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{10}{4}\))<sup>th</sup> item</p> <p>= 2.5<sup>th</sup> item.</p> <p>Then, 2.5<sup>th</sup> item lies in 2<sup>nd</sup> and 3<sup>rd</sup> item.</p> <p>so, Q<sub>1</sub>Median = \(\frac{12+16}{2}\)</p> <p>= \(\frac{28}{2}\)</p> <p>Therefore, Q<sub>1</sub>= 14.</p> <p></p>
Q3:
Find the Quartile(Q1) of the list:
12, 10, 16, 14, 20, 17, 23.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>Now, 10, 12, 14, 16, 17, 20, 23.</p> <p>N=7</p> <p>Q<sub>1</sub> = (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> = (\(\frac{7+1}{4}\))<sup>th</sup> item</p> <p> = 2<sup>th</sup> item.</p> <p>2<sup>th</sup> item lies in 12.</p> <p>Therefore, Q<sub>1</sub> = 12.</p>
Q4:
Find the Quartile(Q3) of the list:
15, 9, 27, 21, 39, 33, 45.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>9, 15, 21, 27, 33, 39, 45.</p> <p>N=7</p> <p>Now, Q<sub>3</sub> =3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= 3(\(\frac{7+1}{4}\))<sup>th</sup> item.</p> <p>= 3\(\times\)2<sup>th</sup> item</p> <p>= 6<sup>th</sup> item.</p> <p>In given data 6<sup>th</sup> item is 39.</p> <p>Therefore, Q<sub>3</sub> = 39.</p>
Q5:
Find the Quartile(Q3) of the list:
26, 14, 22, 18, 38, 30, 34.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>14, 18, 22, 26, 30, 34, 38.</p> <p>N= 7</p> <p>Now, Q<sub>3</sub> = 3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> = 3(\(\frac{7+1}{4}\))<sup>th</sup> item</p> <p> = 3\(\times\)2</p> <p> = 6<sup>th</sup> item.</p> <p>In the given data 6<sup>th</sup> item is 34.</p> <p>Therefore, Q<sub>3</sub>= 34.</p>
Q6:
Find the Quartile(Q3) of the list:
80, 90, 60, 70, 20, 30, 50, .
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>20, 30, 50, 60, 70, 80, 90.</p> <p>N= 7</p> <p>Now, Q<sub>3</sub> = 3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> = 3(\(\frac{7+1}{4}\))<sup>th</sup> item</p> <p> = 3\(\times\)2</p> <p> = 6<sup>th</sup> item.</p> <p>In given data 6<sup>th</sup> item is 80.</p> <p>Therefore, Q<sub>3</sub> = 80.</p>
Q7:
Find the Quartile(Q1) of the list:
Marks(x) |
32 |
36 |
40 |
44 |
48 |
52 |
No of students(f) |
2 |
5 |
9 |
6 |
3 |
2 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <table width="320"><tbody><tr><td>Marks(x)</td> <td>No of Students(f)</td> <td>c.f</td> </tr><tr><td>32</td> <td>2</td> <td>2</td> </tr><tr><td>36</td> <td>5</td> <td>2+5=7</td> </tr><tr><td>40</td> <td>9</td> <td>7+9=16</td> </tr><tr><td>44</td> <td>6</td> <td>16+6=22</td> </tr><tr><td>48</td> <td>3</td> <td>22+3=25</td> </tr><tr><td>52</td> <td>2</td> <td>25+2=27</td> </tr><tr><td>Total</td> <td>N=27</td> <td></td> </tr></tbody></table><p>Now, Q<sub>1</sub> = (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>=(\(\frac{27+1}{4}\))<sup>th</sup> item.</p> <p>= 7<sup>th</sup> item.</p> <p>In c.f Column, the corresponding value of 7 is 36.</p> <p>Therefore, Q<sub>1</sub> = 36</p>
Q8:
Find the Quartile(Q3) of the list:
Marks |
50 |
60 |
70 |
80 |
90 |
100 |
No of workers |
6 |
10 |
15 |
13 |
8 |
3 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <table width="301"><tbody><tr><td>Marks(x)</td> <td>No of workers(f)</td> <td>c.f</td> </tr><tr><td>50</td> <td>6</td> <td>6</td> </tr><tr><td>60</td> <td>10</td> <td>16</td> </tr><tr><td>70</td> <td>15</td> <td>31</td> </tr><tr><td>80</td> <td>13</td> <td>44</td> </tr><tr><td>90</td> <td>8</td> <td>52</td> </tr><tr><td>100</td> <td>3</td> <td>55</td> </tr><tr><td>Total</td> <td>N=55</td> <td></td> </tr></tbody></table><p>Now, Position of Q<sub>3</sub> = 3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= 3(\(\frac{55+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{168}{4}\))<sup>th</sup> item.</p> <p>= 42<sup>th</sup> item.</p> <p>In the given data, 42<sup>th</sup> item is 80.</p> <p>Therefore, Q<sub>3</sub> = 80</p>
Q9:
Find the Quartile(Q1) of the list:
Marks(x) |
22 |
27 |
32 |
37 |
42 |
No of people(f) |
35 |
42 |
40 |
30 |
24 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="274"><tbody><tr><td>Marks(x)</td> <td>No of people(f)</td> <td>c.f)</td> </tr><tr><td>22</td> <td>35</td> <td>35</td> </tr><tr><td>27</td> <td>42</td> <td>77</td> </tr><tr><td>32</td> <td>40</td> <td>117</td> </tr><tr><td>37</td> <td>30</td> <td>147</td> </tr><tr><td>42</td> <td>24</td> <td>171</td> </tr><tr><td>Total</td> <td>N=171</td> <td></td> </tr></tbody></table><p>Now, Q<sub>1</sub> = (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{171+1}{4}\))<sup>th</sup> item.</p> <p>= 43<sup>th</sup> item.</p> <p>In c.f column, 43<sup>th</sup> item is just greater than 35.So, Q<sub>1</sub>lies on the correspondent value of 77.</p> <p>Therefore, Q<sub>1</sub> = 27</p> <p></p>
Q10:
Find the Quartile(Q1) of the list:
Marks |
25 |
30 |
35 |
40 |
45 |
50 |
55 |
60 |
No of students |
2 |
3 |
6 |
10 |
12 |
13 |
3 |
4 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <table width="266"><tbody><tr><td>Marks(x)</td> <td>Number of Students(f)</td> <td>C.f</td> </tr><tr><td>25</td> <td>2</td> <td>2</td> </tr><tr><td>30</td> <td>3</td> <td>2+3=5</td> </tr><tr><td>35</td> <td>6</td> <td>5+6=11</td> </tr><tr><td>40</td> <td>10</td> <td>11+10=21</td> </tr><tr><td>45</td> <td>12</td> <td>21+12=33</td> </tr><tr><td>50</td> <td>13</td> <td>33+13=46</td> </tr><tr><td>55</td> <td>3</td> <td>46+3=49</td> </tr><tr><td>60</td> <td>4</td> <td>49+4=53</td> </tr><tr><td>Total</td> <td>N= 53</td> <td></td> </tr></tbody></table><p>N= 53</p> <p>Now, Position of Q<sub>1</sub>=(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{53+1}{4}\))<sup>th</sup> item.</p> <p>= 13.5<sup>th</sup> item.</p> <p>In the given data, 13.5<sup>th</sup> item lies in 35 and 40.</p> <p>Now, 35+(40-35)\(\times\) 25%</p> <p>= 35+5\(\times\)\(\frac{25}{100}\)</p> <p>= 35 + 5\(\times\)0.25</p> <p>= 35+1.25</p> <p>= 36.25</p> <p>Therefore, Q<sub>1</sub>= 36.25</p>
Q11:
Find the Quartile(Q3) of the list:
x |
100 |
200 |
300 |
400 |
500 |
600 |
700 |
f |
8 |
9 |
7 |
15 |
22 |
12 |
10 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <table width="232"><tbody><tr><td> x</td> <td> f</td> <td> c.f</td> </tr><tr><td> 100</td> <td> 8</td> <td> 8</td> </tr><tr><td> 200</td> <td> 9</td> <td>8+9=17</td> </tr><tr><td> 300</td> <td> 7</td> <td>17+7=24</td> </tr><tr><td> 400</td> <td> 15</td> <td>24+15=39</td> </tr><tr><td> 500</td> <td> 22</td> <td>39+22=61</td> </tr><tr><td> 600</td> <td> 12</td> <td>61+12=73</td> </tr><tr><td> 700</td> <td> 10</td> <td>73+10=83</td> </tr><tr><td> Total</td> <td>N=83</td> <td></td> </tr></tbody></table><p>N=83</p> <p>Now, Q<sub>3</sub> = 3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> = 3(\(\frac{83+1}{4}\))<sup>th</sup> item.</p> <p> = 3\(\times\)21</p> <p> = 63<sup>th</sup> item.</p> <p>In the given data, 63<sup>th</sup> item lies in 600.</p> <p>Therefore, Q<sub>3</sub> = 600.</p> <p></p>
Q12:
Find the Quartile(Q1) of the list:
27, 29, 18, 25, 32, 21, 26.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>27, 29, 18, 25, 32, 21, 26.</p> <p>N= 7</p> <p>Now, Q<sub>1</sub>= (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> =( \(\frac{7+1}{4}\))<sup>th</sup> item</p> <p> = \(\frac{8}{4}\)<sup>th</sup> item.</p> <p> = 2<sup>th</sup> item.</p> <p>Therefore, 2<sup>th</sup> item is 29.</p>
Q13:
Find the Quartile(Q1) of the list:
27, 29, 18, 25, 32, 21, 26.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>18, 21, 25, 26, 27, 29, 32</p> <p>N= 7</p> <p>Now, Q<sub>1</sub>= (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> =( \(\frac{7+1}{4}\))<sup>th</sup> item</p> <p> = \(\frac{8}{4}\)<sup>th</sup> item.</p> <p> = 2<sup>th</sup> item.</p> <p>Therefore, 2<sup>th</sup> item is 21.</p>
Q14:
Find the Quartile(Q3) of the list:
45, 32, 67, 54, 34, 28, 78,.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>28, 32, 34, 45, 54, 60, 67,</p> <p>N=7</p> <p>Now, Q<sub>3</sub> = 3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> = 3(\(\frac{7+1}{4}\))<sup>th</sup> item.</p> <p> = 3\(\times\)2</p> <p> = 6<sup>th</sup> item.</p> <p>In the given data 6<sup>th</sup> item is 60.</p> <p>Therefore, Q<sub>3</sub> = 60.</p> <p><sup></sup></p>
Q15:
Find the Quartile(Q1) of the list:
10, 8, 6, 4, 12, 18, 20.
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order.</p> <p>4, 6, 8, 10, 12, 18, 20.</p> <p>N=7</p> <p>Now, Q<sub>1</sub> = (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p> = (\(\frac{7+1}{4}\))<sup>th</sup>item.</p> <p> = \(\frac{8}{4}\)<sup>th</sup> item.</p> <p> = 2<sup>nd</sup>item.</p> <p>In the given data, 2<sup>nd</sup> item is 6.</p> <p>Therefore, Q<sub>1</sub> = 6.</p>
Q16:
Find the Quartile(Q3) of the list:
Age |
8 |
10 |
12 |
14 |
16 |
18 |
Number of Students |
3 |
5 |
7 |
8 |
3 |
1 |
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <table width="302"><tbody><tr><td>Years(x)</td> <td>Number of Students(f)</td> <td>c.f</td> </tr><tr><td>8</td> <td>3</td> <td>3</td> </tr><tr><td>10</td> <td>5</td> <td>3+5=8</td> </tr><tr><td>12</td> <td>7</td> <td>8+7=15</td> </tr><tr><td>14</td> <td>8</td> <td>15+8=23</td> </tr><tr><td>16</td> <td>3</td> <td>23+3=26</td> </tr><tr><td>18</td> <td>1</td> <td>26+1=27</td> </tr><tr><td>Total</td> <td>N= 27</td> <td></td> </tr></tbody></table><p>Here, N=27</p> <p>Now, Q<sub>3</sub> = 3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= 3(\(\frac{27+1}{4}\))<sup>th</sup> item.<br><br></p> <p>= 3\(\times\)7</p> <p>= 21<sup>st</sup>item.</p> <p>In the given data 21item lies in 14 years.<sup>st</sup>item lies in 14 years.</p> <p>Therefore, Q<sub>3</sub> = 14</p> <p></p>
Q17:
Find the Quartile(Q1) of the list:
Wages |
45 |
55 |
65 |
75 |
85 |
95 |
No of workers |
20 |
25 |
24 |
18 |
15 |
17 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <table width="243"><tbody><tr><td>Wages(x)</td> <td>No of workers(f)</td> <td>c.f</td> </tr><tr><td>45</td> <td>20</td> <td>20</td> </tr><tr><td>55</td> <td>25</td> <td>45</td> </tr><tr><td>65</td> <td>24</td> <td>69</td> </tr><tr><td>75</td> <td>18</td> <td>87</td> </tr><tr><td>85</td> <td>15</td> <td>102</td> </tr><tr><td>95</td> <td>17</td> <td>119</td> </tr><tr><td>Total</td> <td>N= 119</td> <td></td> </tr><tr><td></td> <td></td> <td></td> </tr></tbody></table><p>N=119</p> <p>Now, position of Q<sub>1</sub> = (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{119+1}{4}\))<sup>th</sup> item.</p> <p>= \(\frac{120}{4}\)</p> <p>= 30<sup>th</sup> item.</p> <p>In the given data, 30<sup>th</sup> item lies in 45 c.f.</p> <p>Therefore, Q<sub>1</sub>= 55</p>
Q18:
Find the Quartile(Q3) of the list:
Marks |
10 |
15 |
20 |
25 |
30 |
35 |
No of students |
3 |
7 |
15 |
12 |
7 |
3 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <table width="252"><tbody><tr><td>Marks(x)</td> <td>No of students(f)</td> <td>c.f</td> </tr><tr><td>10</td> <td>3</td> <td>3</td> </tr><tr><td>15</td> <td>7</td> <td>10</td> </tr><tr><td>20</td> <td>15</td> <td>25</td> </tr><tr><td>25</td> <td>12</td> <td>37</td> </tr><tr><td>30</td> <td>7</td> <td>44</td> </tr><tr><td>35</td> <td>3</td> <td>47</td> </tr><tr><td>Total</td> <td>N= 47</td> <td></td> </tr></tbody></table><p>N= 47</p> <p>Q<sub>3</sub>lies in 3(\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= 3(\(\frac{47+1}{4}\))<sup>th</sup> item.</p> <p>= 3\(\times\) 12</p> <p>= 36<sup>th</sup> item.</p> <p>In given data, 36<sup>th</sup> item lies in 25 marks.</p> <p>Therefore, Q<sub>3</sub> = 25</p>
Q19:
Find the quartile(Q1) of the list:
Marks |
24 |
36 |
50 |
65 |
78 |
No of students |
2 |
4 |
12 |
11 |
6 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="202"><tbody><tr><td>Marks(x)</td> <td>No of students(f)</td> <td>c.f</td> </tr><tr><td>24</td> <td>2</td> <td>2</td> </tr><tr><td>36</td> <td>4</td> <td>6</td> </tr><tr><td>50</td> <td>12</td> <td>18</td> </tr><tr><td>65</td> <td>11</td> <td>29</td> </tr><tr><td>78</td> <td>6</td> <td>35</td> </tr><tr><td>Total</td> <td>N= 35</td> <td></td> </tr></tbody></table><p>N= 35</p> <p>Here, Q<sub>1</sub>lies in (\(\frac{N+1}{4}\))<sup>th</sup> item.</p> <p>= (\(\frac{35+1}{4}\))<sup>th</sup> item.</p> <p>= \(\frac{36}{4}\)<sup>th</sup> item.</p> <p>=9<sup>th</sup> item.</p> <p>In the given data, 9<sup>th</sup> item lies in 18 c.f.</p> <p>Therefore, Q<sub>1</sub> = 50</p>
Q20:
Find the first and third quartile of the list:
x |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |
70-80 |
f |
8 |
9 |
7 |
15 |
22 |
12 |
7 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,</p> <p>20-30</p> <table width="234"><tbody><tr><td>x</td> <td>f</td> <td>c.f</td> </tr><tr><td>10-20</td> <td>8</td> <td>8</td> </tr><tr><td>20-30</td> <td>9</td> <td>17</td> </tr><tr><td>30-40</td> <td>7</td> <td>24</td> </tr><tr><td>40-50</td> <td>15</td> <td>39</td> </tr><tr><td>50-60</td> <td>22</td> <td>61</td> </tr><tr><td>60-70</td> <td>12</td> <td>73</td> </tr><tr><td>70-80</td> <td>7</td> <td>80</td> </tr><tr><td></td> <td>N=80</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 ( \(\frac{80}{4}\))<sup>th</sup> item</p> <p>= value of 20<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater than 20 is 24 and its corresponding class is (30-40).</p> <p>\(\therefore\) Q<sub>1</sub> lies in the class 30-40</p> <p>Here,</p> <p>\(\frac{N}{4}\) = 10, l= 30, c.f. =17, f = 7and i =10</p> <p>\(\therefore\)Q<sub>1</sub>= l + \(\frac{\frac{N}{4}− c.f}{f}\) × i</p> <p>= 30 + \(\frac{20−17}{7}\) ×10</p> <p>= 30 + \(\frac{3}{7}\) ×10</p> <p>= 30 +4.28</p> <p>= 34.28</p> <p>Again,</p> <p>Q<sub>3</sub> Class = value of(\(\frac{3N}{4}\))<sup>th</sup> item</p> <p>= value of(\(\frac{3 * 80}{4}\))<sup>th</sup> item</p> <p>=value of 60<sup>th</sup> item</p> <p>In c.f. column, c.f.just greater than 60 is 61 and its corresponding class is 50-60.</p> <p>Here,</p> <p>\(\frac{3N}{4}\) = 60, l= 50, c.f. = 39, f = 22 and i =10</p> <p>\(\therefore\)Q<sub>3</sub>= l + \(\frac{\frac{3N}{4}− c.f}{f}\) × i</p> <p>= 50 + \(\frac{60− 39}{22}\) ×10</p> <p>=50 + \(\frac{21}{22}\) ×10</p> <p>= 50 +9.54</p> <p>=59.54</p>