Subjective Questions
Q1:
Arjun measured all 7 markers in his set of art supplies. They had lengths of:
8.6 centimeters, 8.5 centimeters, 8.5 centimeters, 8.4 centimeters, 8.4 centimeters, 8.1 centimeters, 8.1 centimeters
What was the median length of the markers?
Type: Very_short
Difficulty: Easy
Show/Hide Answer
Answer: <p>First, arrange the numbers from least to greatest:</p> <div> <table><tbody><tr><td>8.1</td> <td></td> <td>8.1</td> <td></td> <td>8.4</td> <td></td> <td>8.4</td> <td></td> <td>8.5</td> <td></td> <td>8.5</td> <td></td> <td>8.6</td> </tr></tbody></table></div> <p>Now find the number in the middle.</p> <table><tbody><tr><td>8.1</td> <td></td> <td>8.1</td> <td></td> <td>8.4</td> <td></td> <td>8.4</td> <td></td> <td>8.5</td> <td></td> <td>8.5</td> <td></td> <td>8.6</td> </tr></tbody></table><p>Hence, The number in the middle is 8.4. The median length of the markers was 8.4 centimeters.</p>
Q2:
What is the median?
-5 -3 -4 -5 -9 -5 -8 0
Type: Short
Difficulty: Easy
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Answer: <p>First, arrange the numbers from least to greatest. Remember that with negative numbers, larger numbers like -9 (if you ignore the minus sign) are less than smaller numbers. </p> <div id="yui_3_14_0_3_1457937806126_76"> <table><tbody><tr><td>-9</td> <td></td> <td>-8</td> <td></td> <td>-5</td> <td></td> <td>-5</td> <td></td> <td>-5</td> <td></td> <td>-4</td> <td></td> <td>-3</td> <td></td> <td>0</td> </tr></tbody></table></div> <p>There is an even number of numbers, so there are two numbers in the middle.</p> <div> <table><tbody><tr><td>-9</td> <td></td> <td>-8</td> <td></td> <td>-5</td> <td></td> <td>-5</td> <td></td> <td>-5</td> <td></td> <td>-4</td> <td></td> <td>-3</td> <td></td> <td>0</td> </tr></tbody></table></div> <p>The median is the mean of the two middle numbers. Find the mean of -5 and -5.</p> <div>-5 + -5 = -10<br>-10 ÷ 2 = -5</div> <div><br>Hence, The median is -5.</div>
Q3:
A mechanic measured the voltage of 9 car batteries. The voltages were:
9.3 volts, 9.8 volts, 9.8 volts, 9.3 volts, 9.3 volts, 9.1 volts, 9.9 volts, 9.5 volts, 9.1 volts
What was the median voltage?
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>First, arrange the numbers from least to greatest:<br><br></p> <div> <table><tbody><tr><td>9.1</td> <td></td> <td>9.1</td> <td></td> <td>9.3</td> <td></td> <td>9.3</td> <td></td> <td>9.3</td> <td></td> <td>9.5</td> <td></td> <td>9.8</td> </tr><tr><td>9.8</td> <td></td> <td>9.9</td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr></tbody></table></div> <p>Now find the number in the middle.</p> <div> <table><tbody><tr><td>9.1</td> <td></td> <td>9.1</td> <td></td> <td>9.3</td> <td></td> <td>9.3</td> <td></td> <td>9.3</td> <td></td> <td>9.5</td> <td></td> <td>9.8</td> </tr><tr><td>9.8</td> <td></td> <td>9.9</td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr></tbody></table></div> <p>The number in the middle is 9.3.</p> <p>Hence, The median voltage was 9.3 volts.</p>
Q4:
Find the median of given data: 10, 14, 16, 20, 22, 25, 28
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Here, Given data is 10 ,14, 16,. 20, 22, 25, 28</p> <p>Numbers of terms(n) = 7</p> <p>We have, Median =( \(\frac{n+1}{2}\))<sup>th </sup>item</p> <p>( \(\frac{7+1}{2}\))<sup>th </sup>item</p> <p>= (\(\frac{8}{2}\))<sup>th</sup> item</p> <p>= 4<sup>th</sup> item</p> <p>\(\therefore\) The median of the given data is 20.</p>
Q5:
Find the median of the given data: 2, 16, 12, 10, 24, 28, 30, 32
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>Arranging the data in ascending order</p> <p>10, 12, 16, 20, 24, 28 , 30, 32</p> <p>Number of terms(n) = 8</p> <p>We have,</p> <p>Median = (\(\frac{n+1}{2}\))<sup>th</sup> item</p> <p>= (\(\frac{8+1}{2}\))<sup>th</sup> item</p> <p>= (\(\frac{9}{2}\))<sup>th</sup> item</p> <p>= (4.5)<sup>th</sup> item</p> <p>Now,</p> <p>Median = mean of 4<sup>th</sup> item and 5<sup>th</sup> item</p> <p>= \(\frac{20+24}{2}\)</p> <p>= \(\frac{44}{2}\)</p> <p>= 22</p> <p>\(\therefore\) Median = 22</p>
Q6:
Find the median of the given data:
x |
10 |
15 |
20 |
25 |
30 |
f |
2 |
4 |
6 |
5 |
4 |
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="170"><tbody><tr><td>x</td> <td>f</td> <td>c.f</td> </tr><tr><td>10</td> <td>2</td> <td>2</td> </tr><tr><td>15</td> <td>4</td> <td>6</td> </tr><tr><td>20</td> <td>6</td> <td>12</td> </tr><tr><td>25</td> <td>5</td> <td>17</td> </tr><tr><td>30</td> <td>4</td> <td>21</td> </tr><tr><td></td> <td>N = 21</td> <td></td> </tr></tbody></table><p>We have,</p> <p>Median = value of (\(\frac{n+1}{2}\))<sup>th</sup> item</p> <p>= value of (\(\frac{21+1}{2}\))<sup>th</sup> item</p> <p>= value of 11<sup>th</sup> item</p> <p>In c.f. just greater than 11 is 12 and its corresponding value is 20.</p> <p>\(\therefore\) Median is 20.</p>
Q7:
Find the median from the given data:
Age (in yrs) |
0-4 |
4-8 |
8-12 |
12-16 |
16-20 |
No. of students |
2 |
4 |
8 |
6 |
2 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="229"><tbody><tr><td>Class</td> <td>Frequency</td> <td>c.f.</td> </tr><tr><td>0-4</td> <td>2</td> <td>2</td> </tr><tr><td>4-8</td> <td>4</td> <td>6</td> </tr><tr><td>8-12</td> <td>8</td> <td>14</td> </tr><tr><td>12-16</td> <td>6</td> <td>20</td> </tr><tr><td>16-20</td> <td>2</td> <td>22</td> </tr><tr><td></td> <td>N=22</td> <td></td> </tr></tbody></table><p></p> <p>Here, \(\frac{N}{2}\) = \(\frac{22}{2}\) =11</p> <p>Median Class = value of (\(\frac{N}{2}\))<sup>th</sup> item</p> <p>= (11)<sup>th</sup> item</p> <p>= (8-12)</p> <p>Here,</p> <p><em>l</em> = 8, (\(\frac{N}{2}\))<sup>th</sup> item = 11, c.f.= 6, f = 8, i= 4</p> <p>Now,</p> <p>median = l + \(\frac{\frac{N}{2}− c.f}{f}\) × i</p> <p>= 8 + \(\frac{11−6}{8}\) ×4</p> <p>= 8+\(\frac{5}{8}\) ×4</p> <p>= 8+ 2.5</p> <p>= 10.5</p> <p>\(\therefore\) median =10.5</p> <p></p>
Q8:
Find the median from the given data:
Marks |
5-10 |
10-15 |
15-20 |
20-25 |
25-30 |
Frequency |
20 |
30 |
50 |
40 |
10 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="231"><tbody><tr><td>Marks</td> <td>Frequency</td> <td>c.f.</td> </tr><tr><td>5-10</td> <td>20</td> <td>20</td> </tr><tr><td>10-15</td> <td>30</td> <td>50</td> </tr><tr><td>15-20</td> <td>50</td> <td>100</td> </tr><tr><td>20-25</td> <td>40</td> <td>140</td> </tr><tr><td>25-30</td> <td>10</td> <td>150</td> </tr><tr><td></td> <td>N=150</td> <td></td> </tr></tbody></table><p></p> <p>Here, \(\frac{N}{2}\) = \(\frac{150}{2}\) =75</p> <p>Median Class = value of (\(\frac{N}{2}\))<sup>th</sup> item</p> <p>= (75)<sup>th</sup> item</p> <p>= (15-20)</p> <p><em>l</em> = 15, (\(\frac{N}{2}\))<sup>th</sup> item = 75, c.f.= 50, f = 50, i= 5</p> <p>Now,</p> <p>median = l + \(\frac{\frac{N}{2}− c.f}{f}\) × i</p> <p>=15 + \(\frac{75−50}{50}\) ×5</p> <p>= 15+\(\frac{25}{50}\) ×5</p> <p>= 15+2.5</p> <p>= 17.5</p> <p>\(\therefore\) median =17.5</p> <p></p>
Q9:
Find the median from the given data:
x |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |
f |
3 |
6 |
8 |
10 |
15 |
12 |
6 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="225"><tbody><tr><td>x</td> <td>f</td> <td>c.f.</td> </tr><tr><td>0-10</td> <td>3</td> <td>3</td> </tr><tr><td>10-20</td> <td>6</td> <td>9</td> </tr><tr><td>20-30</td> <td>8</td> <td>17</td> </tr><tr><td>30-40</td> <td>10</td> <td>27</td> </tr><tr><td>40-50</td> <td>15</td> <td>42</td> </tr><tr><td>50-60</td> <td>12</td> <td>54</td> </tr><tr><td>60-70</td> <td>6</td> <td>60</td> </tr><tr><td></td> <td>N=60</td> <td></td> </tr></tbody></table><p></p> <p>Here, \(\frac{N}{2}\) = \(\frac{60}{2}\) =30</p> <p>Median Class = value of (\(\frac{N}{2}\))<sup>th</sup> item</p> <p>= (30)<sup>th</sup> item</p> <p>= (40-50)</p> <p>Here,</p> <p><em>l</em> = 40, (\(\frac{N}{2}\))<sup>th</sup> item = 30, c.f.= 27, f =15, i=10</p> <p>Now,</p> <p>median = l + \(\frac{\frac{N}{2}− c.f}{f}\) × i</p> <p>=40 + \(\frac{30−27}{15}\) ×10</p> <p>= 40+\(\frac{3}{15}\) ×10</p> <p>= 40+2</p> <p>= 42</p> <p>\(\therefore\) median = 42</p> <p></p>
Q10:
Find the median from the given data:
x
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
60-70
|
f
|
5
|
8
|
11
|
15
|
20
|
12
|
9
|
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="225"><tbody><tr><td> <p>x</p> </td> <td width="56"> <p>f</p> </td> <td width="52"> <p>c.f.</p> </td> </tr><tr><td> <p>0-10</p> </td> <td width="56"> <p>5</p> </td> <td width="52"> <p>5</p> </td> </tr><tr><td> <p>10-20</p> </td> <td width="56"> <p>8</p> </td> <td width="52"> <p>13</p> </td> </tr><tr><td> <p>20-30</p> </td> <td width="56"> <p>11</p> </td> <td width="52"> <p>24</p> </td> </tr><tr><td> <p>30-40</p> </td> <td width="56"> <p>15</p> </td> <td width="52"> <p>39</p> </td> </tr><tr><td> <p>40-50</p> </td> <td width="56"> <p>20</p> </td> <td width="52"> <p>59</p> </td> </tr><tr><td> <p>50-60</p> </td> <td width="56"> <p>12</p> </td> <td width="52"> <p>71</p> </td> </tr><tr><td> <p>60-70</p> </td> <td width="56"> <p>9</p> </td> <td width="52"> <p>80</p> </td> </tr><tr><td></td> <td width="56"> <p>N=80</p> </td> <td width="52"></td> </tr></tbody></table><p></p> <p>Here, \(\frac{N}{2}\) = \(\frac{80}{2}\) =40</p> <p>Median Class = value of (\(\frac{N}{2}\))<sup>th</sup>item</p> <p>= (40)<sup>th</sup>item</p> <p>= (40-50)</p> <p>Here,</p> <p><em>l</em>= 40, (\(\frac{N}{2}\))<sup>th</sup>item = 40, c.f.= 39, f =20, i=10</p> <p>Now,</p> <p>median = l + \(\frac{\frac{N}{2}− c.f}{f}\) × i</p> <p>= 40 + \(\frac{40−39}{20}\) ×10</p> <p>= 40+\(\frac{1}{20}\) ×10</p> <p>= 40+0.5</p> <p>= 40.5</p> <p>\(\therefore\) median =40.5</p>
Q11:
Find the median from the given data:
x
|
10
|
16
|
20
|
25
|
30
|
35
|
50
|
f
|
4
|
6
|
10
|
15
|
20
|
12
|
8
|
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="161"><tbody><tr><td width="50"> <p>x</p> </td> <td width="52"> <p>f</p> </td> <td width="51"> <p>c.f.</p> </td> </tr><tr><td width="50"> <p>10</p> </td> <td width="52"> <p>4</p> </td> <td width="51"> <p>4</p> </td> </tr><tr><td width="50"> <p>16</p> </td> <td width="52"> <p>6</p> </td> <td width="51"> <p>10</p> </td> </tr><tr><td width="50"> <p>20</p> </td> <td width="52"> <p>10</p> </td> <td width="51"> <p>20</p> </td> </tr><tr><td width="50"> <p>25</p> </td> <td width="52"> <p>15</p> </td> <td width="51"> <p>35</p> </td> </tr><tr><td width="50"> <p>30</p> </td> <td width="52"> <p>20</p> </td> <td width="51"> <p>55</p> </td> </tr><tr><td width="50"> <p>35</p> </td> <td width="52"> <p>12</p> </td> <td width="51"> <p>67</p> </td> </tr><tr><td width="50"> <p>50</p> </td> <td width="52"> <p>8</p> </td> <td width="51"> <p>75</p> </td> </tr><tr><td width="50"> <p></p> </td> <td width="52"> <p>N=75</p> </td> <td width="51"> <p></p> </td> </tr></tbody></table><p></p> <p>We have, = value of (\(\frac{N+1}{2}\))<sup>th</sup> item</p> <p>= value of (\(\frac{75+1}{2}\))<sup>th</sup> item</p> <p>= value of 38<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater then 38 is 55 and its corresponding value is 30.</p> <p>\(\therefore\) Median = 30</p>
Q12:
Find the median from the given data:
Marks
|
80
|
75
|
60
|
55
|
50
|
40
|
35
|
no. of students
|
3
|
7
|
10
|
6
|
4
|
2
|
1
|
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="155"><tbody><tr><td width="44"> <p>Marks</p> </td> <td width="52"> <p>f</p> </td> <td width="51"> <p>c.f.</p> </td> </tr><tr><td width="44"> <p>80</p> </td> <td width="52"> <p>3</p> </td> <td width="51"> <p>3</p> </td> </tr><tr><td width="44"> <p>75</p> </td> <td width="52"> <p>7</p> </td> <td width="51"> <p>10</p> </td> </tr><tr><td width="44"> <p>60</p> </td> <td width="52"> <p>10</p> </td> <td width="51"> <p>20</p> </td> </tr><tr><td width="44"> <p>55</p> </td> <td width="52"> <p>6</p> </td> <td width="51"> <p>26</p> </td> </tr><tr><td width="44"> <p>50</p> </td> <td width="52"> <p>4</p> </td> <td width="51"> <p>30</p> </td> </tr><tr><td width="44"> <p>40</p> </td> <td width="52"> <p>2</p> </td> <td width="51"> <p>32</p> </td> </tr><tr><td width="44"> <p>35</p> </td> <td width="52"> <p>1</p> </td> <td width="51"> <p>33</p> </td> </tr><tr><td width="44"> <p></p> </td> <td width="52"> <p>N=33</p> </td> <td width="51"> <p></p> </td> </tr></tbody></table><p></p> <p>We have, = value of (\(\frac{N+1}{2}\))<sup>th</sup> item</p> <p>= value of (\(\frac{33+1}{2}\))<sup>th</sup> item</p> <p>= value of 17<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater then 17 is 20 and its corresponding value is 60.</p> <p>\(\therefore\) Median = 60</p>
Q13:
Find the median from the given data:
height (cm)
|
110
|
115
|
120
|
124
|
128
|
130
|
no. of girls
|
3
|
5
|
10
|
7
|
3
|
2
|
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p><br></p> <p>We have, = value of (\(\frac{N+1}{2}\))<sup>th</sup> item</p> <p>= value of (\(\frac{40+1}{2}\))<sup>th</sup> item</p> <p>= value of 20.5<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater then 20.5 is 28 and its corresponding value is 120.</p> <p>\(\therefore\) Median = 120</p>
Q14:
Find the median from the given data:
class interval
|
0-5
|
5-10
|
10-15
|
15-20
|
20-25
|
25-30
|
frequency
|
5
|
9
|
15
|
22
|
18
|
11
|
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="251"><tbody><tr><td> <p>x</p> </td> <td width="56"> <p>f</p> </td> <td width="52"> <p>c.f.</p> </td> </tr><tr><td> <p>0-5</p> </td> <td width="56"> <p>5</p> </td> <td width="52"> <p>5</p> </td> </tr><tr><td> <p>5-10</p> </td> <td width="56"> <p>9</p> </td> <td width="52"> <p>14</p> </td> </tr><tr><td> <p>10-15</p> </td> <td width="56"> <p>15</p> </td> <td width="52"> <p>29</p> </td> </tr><tr><td> <p>15-20</p> </td> <td width="56"> <p>22</p> </td> <td width="52"> <p>51</p> </td> </tr><tr><td> <p>20-25</p> </td> <td width="56"> <p>18</p> </td> <td width="52"> <p>69</p> </td> </tr><tr><td> <p>25-30</p> </td> <td width="56"> <p>11</p> </td> <td width="52"> <p>80</p> </td> </tr><tr><td></td> <td width="56"> <p>N=80</p> </td> <td width="52"></td> </tr></tbody></table><p></p> <p>Here, \(\frac{N}{2}\) = \(\frac{80}{2}\) =40</p> <p>Median Class = value of (\(\frac{N}{2}\))<sup>th</sup>item</p> <p>= (40)<sup>th</sup>item</p> <p>= (15-20)</p> <p>Here,</p> <p><em>l</em>= 15, (\(\frac{N}{2}\))<sup>th</sup>item = 40, c.f.= 29, f =22, i=5</p> <p>Now,</p> <p>median = l + \(\frac{\frac{N}{2}− c.f}{f}\) × i</p> <p>= 40 + \(\frac{40−29}{22}\) ×5</p> <p>= 40+\(\frac{11}{22}\) ×5</p> <p>=40+2.5</p> <p>=42.5</p> <p>\(\therefore\) median = 42.5</p>
Q15:
Find the median from the given data:
x
|
10
|
20
|
30
|
40
|
50
|
f
|
4
|
6
|
10
|
8
|
5
|
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="161"><tbody><tr><td width="50"> <p>x</p> </td> <td width="52"> <p>f</p> </td> <td width="51"> <p>c.f.</p> </td> </tr><tr><td width="50"> <p>10</p> </td> <td width="52"> <p>4</p> </td> <td width="51"> <p>4</p> </td> </tr><tr><td width="50"> <p>20</p> </td> <td width="52"> <p>6</p> </td> <td width="51"> <p>10</p> </td> </tr><tr><td width="50"> <p>30</p> </td> <td width="52"> <p>10</p> </td> <td width="51"> <p>20</p> </td> </tr><tr><td width="50"> <p>40</p> </td> <td width="52"> <p>8</p> </td> <td width="51"> <p>28</p> </td> </tr><tr><td width="50"> <p>50</p> </td> <td width="52"> <p>5</p> </td> <td width="51"> <p>33</p> </td> </tr><tr><td width="50"> <p></p> </td> <td width="52"> <p>N=33</p> </td> <td width="51"> <p></p> </td> </tr></tbody></table><p></p> <p>We have, = value of (\(\frac{N+1}{2}\))<sup>th</sup> item</p> <p>= value of (\(\frac{33+1}{2}\))<sup>th</sup> item</p> <p>= value of 17<sup>th</sup> item</p> <p>In c.f. column, c.f. just greater then 17 is 20 and its corresponding value is 30.</p> <p>\(\therefore\) Median = 30</p>