Subjective Questions
Q1:
Rudy volunteered to stamp hands at the entrance of a museum 8 times this year. The number of visitors each time was:
3 visitors, 1 visitor, 3 visitors, 4 visitors, 4 visitors, 4 visitors, 2 visitors, 3 visitors
Type: Very_short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Sum of given terms (\(\sum\)x) =</p> <p>3visitors + 1visitor + 3visitors + 4visitors + 4visitors + 4visitors + 2visitors + 3visitors</p> <p>= 24</p> <p>numbers of terms (n) = 8</p> <p>We have,</p> <p>Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)</p> <p>= \(\frac{24}{8}\)</p> <p>=3</p> <p>Hence, The number of visitors each time was 3</p>
Q2:
Find the mean of the follwoing data.
12, 15, 18, 19, 15, 17, 16, 10, 13, 15
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Now,<br>Sum of a numbers = 12 + 15 + 18 + 19 + 15 + 17 + 16 + 10 + 13 + 15<br>= 150<br>number = 10<br>We know that,<br>or, Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)<br>or,Mean (\(\overline{X}\)) = \(\frac{150}{10}\)<br>\(\therefore\) Mean (\(\overline{X}\)) = 15</p>
Q3:
Find the mean driving speed for 6 different cars on the same highway.
66 mph, 57 mph, 71 mph, 54 mph, 69 mph, 58 mph
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Sum of given terms (\(\sum\)x) = 66 mph + 57 mph + 71 mph + 54 mph + 69 mph + 58 mph = 375</p> <p>numbers of terms (n) = 6</p> <p>We have,</p> <p>Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)</p> <p>= \(\frac{375}{6}\)</p> <p>= 62.5</p> <p>The mean driving speed is 62.5 mph.</p> <p></p>
Q4:
Teacher took 7 math tests in one marking period. What is the mean test score?
9, 73, 84, 91, 87, 77, 94
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Sum of given terms (\(\sum\)x) = 89+ 73+ 84+ 91+ 87+ 77+ 94 = 515</p> <p>numbers of terms (n) =7</p> <p>We have,</p> <p>Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)</p> <p>= \(\frac{515}{7}\)</p> <p>= 73.57</p> <p>Hence, The mean test score is 73.57</p>
Q5:
The Shrestha family drove through 4 midwestern states on their summer vacation. Gasoline prices varied from state to state. What is the mean gasoline price?
$1.79, $1.61, $1.96, $2.08
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Sum of given terms (\(\sum\)x) = $1.79+ $1.61+ $1.96+ $2.08 = $7.44</p> <p>numbers of terms (n) = 4</p> <p>We have,</p> <p>Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)</p> <p>= \(\frac{7.44}{7}\)</p> <p>= 1.86</p> <p>Hence, The mean gasoline price is $1.86</p>
Q6:
The mean of 3, 7, 10, 15 and x is 12, find he value of x.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Now,<br>Sum of numbers = 3 + 7 + 10 + 15 + x<br>= 35 + x<br>We know that,<br>or, Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)<br>or, \(\frac{12}{1}\)= \(\frac{35 + x}{n}\)<br>or, 60 = 35 + x<br>or, x = 60 - 35<br>or, x = 25<br>\(\therefore\) The value of x is 25.</p>
Q7:
Find the mean swimming time rounded to the nearest tenth:
2.6 min, 7.2 min, 3.5 min, 9.8 min, 2.5 min
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Sum of given terms (\(\sum\)x) = 2.6 min+ 7.2 min+ 3.5 min+ 9.8 min+ 2.5 min =25.6</p> <p>numbers of terms (n) =5</p> <p>We have,</p> <p>Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)</p> <p>= \(\frac{25.6}{5}\)</p> <p>= 5.12</p> <p>Hence, The mean swimming time to the nearest tenth is 5.12 min.</p>
Q8:
A marathon race was completed by 5 participants in the times given below. What is the mean race time for this marathon?
2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Sum of given terms (\(\sum\)x) =</p> <p>2.7 hr + 8.3 hr + 3.5 hr + 5.1 hr + 4.9 hr = 24.5hr</p> <p>numbers of terms (n) =5</p> <p>We have,</p> <p>Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)</p> <p>= \(\frac{24.5}{5}\)</p> <p>= 4.9</p> <p>Hence, The mean race time is 4.9 hr</p>
Q9:
The mean of m, m+2, m+4, m+6, and m+8 is 13, find the value of m.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Now,<br>Sum of number =m + m+2 + m+4 + m+6 + m+8<br>= 5m + 20<br>We know that,<br>or, Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)<br>or, \(\frac{13}{1}\) = \(\frac{5m + 20}{5}\)<br>or, 65 = 5m + 20<br>or, 5m = 65 - 20<br>or, 5m = 45<br>or, m = \(\frac{45}{5}\)<br>or, m = 9<br>\(\therefore\) The value of m is 9.<br><br></p>
Q10:
If the mean of y, y+3, y+7, y+10, y+13 and y+15 is 18, find the value of y.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Now,<br>Sum of a numbers =y + y+3 + y+7 + y+10 + y+13 + y+15<br>= 6y + 48<br>We know that,<br>or, Mean (\(\overline{X}\)) = \(\frac{\sum{x}}{n}\)<br>or, 18 = \(\frac{6y + 48}{6}\)<br>or, 108 = 6y + 48<br>or, 108 - 48 = 6y<br>or, 6y = 60<br>or, y = \(\frac{60}{6}\)<br>or, y = 10<br>\(\therefore\) The value of y is 10.<br><br><br></p>
Q11:
Find the mean of the following data.
| x |
5 |
10 |
15 |
20 |
25 |
| f |
2 |
6 |
10 |
5 |
2 |
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="65"><tbody><tr><td>x</td> <td>f</td> <td>fx</td> </tr><tr><td>5</td> <td>2</td> <td>10</td> </tr><tr><td>10</td> <td>6</td> <td>60</td> </tr><tr><td>15</td> <td>10</td> <td>150</td> </tr><tr><td>20</td> <td>5</td> <td>100</td> </tr><tr><td>25</td> <td>2</td> <td>50</td> </tr><tr><td>Total</td> <td>25</td> <td>370</td> </tr></tbody></table><p>Now,<br>or, \(\overline{X}\) = \(\frac{\sum{x}}{n}\)<br>or, \(\overline{X}\) = \(\frac{370}{25}\)<br>\(\therefore\) \(\overline{X}\) = 14.8</p>
Q12:
Find the mean of the following continuous data.
| Class Interval |
0 -6 |
6 -12 |
12 - 18 |
18 - 24 |
24 - 30 |
| Frequency |
2 |
4 |
10 |
6 |
2 |
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="460"><tbody><tr><td>Class Interval</td> <td>frequency</td> <td>Mid-Value</td> <td>F.x</td> </tr><tr><td>0 - 6</td> <td>32</td> <td>3</td> <td>96</td> </tr><tr><td>6 - 12</td> <td>4</td> <td>9</td> <td>36</td> </tr><tr><td>12 - 18</td> <td>10</td> <td>15</td> <td>150</td> </tr><tr><td>18 - 24</td> <td>6</td> <td>21</td> <td>126</td> </tr><tr><td>24 - 30</td> <td>2</td> <td>27</td> <td>54</td> </tr><tr><td></td> <td>N = 24</td> <td></td> <td>\(\sum{fx}\) = 372</td> </tr></tbody></table><p>We know that,<br>or, \(\overline{X}\) = \(\frac{\sum{fx}}{N}\)<br>or, \(\overline{X}\) = \(\frac{372}{24}\)<br>\(\therefore\)\(\overline{X}\) =15.5</p>
Q13:
The mean of the given data is 21. Find the value of p.
| class interval |
0 -8 |
8 - 16 |
16 - 24 |
24 - 32 |
32 - 40 |
| frequency |
5 |
9 |
10 |
p |
8 |
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="519"><tbody><tr><td>class interval</td> <td>x </td> <td>f</td> <td>fx</td> </tr><tr><td>0 - 8</td> <td>4</td> <td>5</td> <td>20</td> </tr><tr><td>8 - 16</td> <td>12</td> <td>9</td> <td>108</td> </tr><tr><td>16 - 24</td> <td>10</td> <td>10</td> <td>200</td> </tr><tr><td>24 - 32</td> <td>28</td> <td>p</td> <td>28 + p</td> </tr><tr><td>32 - 40</td> <td>36</td> <td>8</td> <td>288</td> </tr><tr><td></td> <td></td> <td>N = 32 + p</td> <td>\(\sum{fx}\) = 616 + 28p</td> </tr></tbody></table><p>we know that,<br>or, \(\overline{X}\) = \(\frac{\sum{fx}}{N}\)<br>or, 21= \(\frac{616 + 28p}{32 + p}\)<br>or, 672 + 21p = 616 + 28p<br>or, 672 - 616 = 28p - 21p<br>or, 56 = 7p<br>or, p = \(\frac{56}{7}\)<br>or, p = 8<br>\(\therefore\) The required mean is 8.</p>
Q14:
Find the mean of the following data.
| Weight (in kg) |
20 |
24 |
30 |
32 |
35 |
| No. of students |
4 |
6 |
8 |
5 |
2 |
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="267"><tbody><tr><td>Weight</td> <td>No. of students</td> <td>fx</td> </tr><tr><td>20</td> <td>4</td> <td>80</td> </tr><tr><td>24</td> <td>6</td> <td>144</td> </tr><tr><td>30</td> <td>8</td> <td>240</td> </tr><tr><td>32</td> <td>5</td> <td>160</td> </tr><tr><td>35</td> <td>3</td> <td>70</td> </tr><tr><td></td> <td>N = 26</td> <td>\(\sum{fx}\) = 694</td> </tr></tbody></table><p>We know that,<br>or, \(\overline{X}\) = \(\frac{\sum{fx}}{N}\)<br>or, \(\overline{X}\) = \(\frac{694}{26}\)<br>\(\therefore\) \(\overline{X}\) = 26.69 kg<br><br><br><br></p>
Q15:
Find the mean of the following continuous data.
|
marks obtained
|
10 -20
|
20 - 30
|
30 - 40
|
40 - 50
|
50 - 60
|
|
No. of students
|
4
|
6
|
10
|
3
|
2
|
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="316"><tbody><tr><td> <p>Marks</p> </td> <td> <p>Students</p> </td> <td> <p>mid-value</p> </td> <td> <p>fx</p> </td> </tr><tr><td> <p>10 - 20</p> </td> <td> <p>4</p> </td> <td> <p>15</p> </td> <td> <p>60</p> </td> </tr><tr><td> <p>20 - 30</p> </td> <td> <p>6</p> </td> <td> <p>25</p> </td> <td> <p>150</p> </td> </tr><tr><td> <p>30 - 40</p> </td> <td> <p>10</p> </td> <td> <p>35</p> </td> <td> <p>350</p> </td> </tr><tr><td> <p>40 - 50</p> </td> <td> <p>3</p> </td> <td> <p>45</p> </td> <td> <p>135</p> </td> </tr><tr><td> <p>50 - 60</p> </td> <td> <p>2</p> </td> <td> <p>55</p> </td> <td> <p>110</p> </td> </tr><tr><td></td> <td> <p>N = 25</p> </td> <td></td> <td> <p>\(\sum{fx}\) = 805</p> </td> </tr></tbody></table><p>We know that,<br> or, \(\overline{X}\) = \(\frac{\sum{fx}}{N}\)<br> or, \(\overline{X}\) = \(\frac{372}{25}\)<br> \(\therefore\) \(\overline{X}\) =14.88</p>
Q16:
Find the mean of the following data.
|
Height (in cm)
|
58
|
60
|
62
|
64
|
66
|
68
|
|
No. of plants
|
12
|
14
|
20
|
13
|
8
|
5
|
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="257"><tbody><tr><td> <p>Height</p> </td> <td> <p>No. of plants</p> </td> <td> <p>fx</p> </td> </tr><tr><td> <p>58</p> </td> <td> <p>12</p> </td> <td> <p>696</p> </td> </tr><tr><td> <p>60</p> </td> <td> <p>14</p> </td> <td> <p>840</p> </td> </tr><tr><td> <p>62</p> </td> <td> <p>20</p> </td> <td> <p>1240</p> </td> </tr><tr><td> <p>64</p> </td> <td> <p>13</p> </td> <td> <p>832</p> </td> </tr><tr><td> <p>66</p> </td> <td> <p>8</p> </td> <td> <p>528</p> </td> </tr><tr><td> <p>68</p> </td> <td> <p>5</p> </td> <td> <p>340</p> </td> </tr><tr><td></td> <td> <p>N = 72</p> </td> <td> <p>\(\sum{fx}\) = 4478</p> </td> </tr></tbody></table><p>We know that,<br> or, \(\overline{X}\) = \(\frac{\sum{fx}}{N}\)<br> or, \(\overline{X}\) = \(\frac{4478}{72}\)<br> \(\therefore\) \(\overline{X}\) = 62.19 cm</p>
Q17:
Find the mean of the following continuous data.
|
Marks
|
5 - 10
|
10 - 15
|
15 - 20
|
20 - 25
|
25 - 30
|
|
No. of students
|
2
|
4
|
8
|
6
|
4
|
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="343"><tbody><tr><td> <p>Marks</p> </td> <td> <p>Students</p> </td> <td> <p>Mid-Value</p> </td> <td> <p>fx</p> </td> </tr><tr><td> <p>5 - 10</p> </td> <td> <p>2</p> </td> <td> <p>7.5</p> </td> <td> <p>15</p> </td> </tr><tr><td> <p>10 - 15</p> </td> <td> <p>4</p> </td> <td> <p>12.5</p> </td> <td> <p>50</p> </td> </tr><tr><td> <p>15 - 20</p> </td> <td> <p>8</p> </td> <td> <p>17.5</p> </td> <td> <p>140</p> </td> </tr><tr><td> <p>20 - 25</p> </td> <td> <p>6</p> </td> <td> <p>22.5</p> </td> <td> <p>135</p> </td> </tr><tr><td> <p>25 - 30</p> </td> <td> <p>4</p> </td> <td> <p>27.5</p> </td> <td> <p>110</p> </td> </tr><tr><td></td> <td> <p>N = 24</p> </td> <td></td> <td> <p>\(\sum{fx}\) = 450</p> </td> </tr></tbody></table><p>We know that,<br> or, \(\overline{X}\) = \(\frac{\sum{fx}}{N}\)<br> or, \(\overline{X}\) = \(\frac{450}{24}\)<br> \(\therefore\) \(\overline{X}\) = 18.75</p>
