"> FR "> For Group A : <br><div class="hscrollenable"> <table border> <tr> <th>Marks</th> <th>Mid values <br> x i </th> <th> f i </th> <th> u i = x i − 45 10 </th> <th> f i u i </th> <th> f i u i 2 </th> </tr> <tr> <td>10 - 25</td> <td> 15</td> <td> 9</td> <td> - 3</td> <td>- 27</td> <td> 81</td> </tr> <tr> <td>20 - 30</td> <td>25</td> <td>17</td> <td> - 2</td> <td>- 34</td> <td> 68</td> </tr> <tr> <td>30 - 40</td> <td> 35</td> <td> 32</td> <td> - 1</td> <td>- 32</td> <td>32</td> </tr> <tr> <td> 40 - 50</td> <td> 45</td> <td>33</td> <td>0</td> <td>0</td> <td> 0</td> </tr> <tr> <td> 50 - 60</td> <td> 55</td> <td>40</td> <td>1</td> <td> 40</td> <td>40</td> </tr> <tr> <td>60 - 70</td> <td>65</td> <td> 10</td> <td>2</td> <td> 20</td> <td> 40</td> </tr> <tr> <td> 70 - 80</td> <td>75</td> <td> 9</td> <td>3</td> <td> 27</td> <td>91</td> </tr> <tr> <td> </td> <td> </td> <td> 150</td> <td> </td> <td> - 6</td> <td> 342</td> </tr> </table></div> <br> Let assumed mean (A) = 45 <br> Mean ( − x ) = A + Σ f i u i N × h = 45 - 6 150 × 10 = 45 - 0.4 = 44.6<br> Standard deviation ( σ 1 ) = h N √ N Σ f i u i 2 − ( Σ f i u i ) 2 = 10 1580 √ 150 × 342 − ( − 6 ) 2 = 1 15 √ 51300 − 36 <br> = 1 15 × 226.41 = 15.09 <br> For Group B : <br> <div class="hscrollenable"> <table border> <tr> <th>Marks</th> <th>Mid values <br> x i </th> <th> f i </th> <th> u i = x i − 45 10 </th> <th> f i u i </th> <th> f i u i 2 </th> </tr> <tr> <td>10 - 25</td> <td> 15</td> <td> 10</td> <td> - 3</td> <td>- 30</td> <td> 90</td> </tr> <tr> <td>20 - 30</td> <td>25</td> <td>20</td> <td> - 2</td> <td>- 40</td> <td> 80</td> </tr> <tr> <td>30 - 40</td> <td> 35</td> <td> 30</td> <td> - 1</td> <td>- 30</td> <td>30</td> </tr> <tr> <td> 40 - 50</td> <td> 45</td> <td>25</td> <td>0</td> <td>0</td> <td> 0</td> </tr> <tr> <td> 50 - 60</td> <td> 55</td> <td>43</td> <td>1</td> <td> 43</td> <td>43</td> </tr> <tr> <td>60 - 70</td> <td>65</td> <td> 15</td> <td>2</td> <td> 30</td> <td> 60</td> </tr> <tr> <td> 70 - 80</td> <td>75</td> <td> 7</td> <td>3</td> <td> 21</td> <td>63</td> </tr> <tr> <td> </td> <td> </td> <td> 150</td> <td> </td> <td> - 6</td> <td> 366</td> </tr> </table> <br> Mean ( − x ) 2 = A + Σ f i u i N × h = 45 - 6 150 × 10 = 45 - 0.4 = 44.6 <br> Standard deviation ( σ 2 ) = h N √ N Σ f i u i 2 − ( Σ f i u i ) 2 = 10 150 √ 150 × 366 − ( − 6 ) 2 = 1 15 √ 54900 − 36 <br> = 1 15 × 234.23 = 15.61 <br> The group which have greater S.D. is more variable. Thus group B is more variable. NC TEX STEX" >


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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 23
Total: 34
From the data given below state which group is more variable, A or B?
MarksGroup A Group B
10 - 209 10
20 - 30 17 20
30 - 40 32 30
40 - 50 33 25
50 - 60 40 43
60 - 70 1015
70 - 809 7

Solution:  
For Group A :
Marks Mid values
xi		 fi ui =
xi−45
10
 fiui fiui2
10 - 25 15 9 - 3 - 27 81
20 - 30 25 17 - 2 - 34 68
30 - 40 35 32 - 1 - 32 32
40 - 50 45 33 0 0 0
50 - 60 55 40 1 40 40
60 - 70 65 10 2 20 40
70 - 80 75 9 3 27 91
150 - 6 342

Let assumed mean (A) = 45
Mean (
−
x
) = A +
Σfiui
N
 × h = 45 -
6
150
 × 10 = 45 - 0.4 = 44.6
Standard deviation (σ1) =
h
N
√NΣfiui2−(Σfiui)2 =
10
1580
√150×342−(−6)2 =
1
15
√51300−36
=
1
15
 × 226.41 = 15.09
For Group B :
Marks Mid values
xi		 fi ui =
xi−45
10
 fiui fiui2
10 - 25 15 10 - 3 - 30 90
20 - 30 25 20 - 2 - 40 80
30 - 40 35 30 - 1 - 30 30
40 - 50 45 25 0 0 0
50 - 60 55 43 1 43 43
60 - 70 65 15 2 30 60
70 - 80 75 7 3 21 63
150 - 6 366

Mean (
−
x
)2 = A +
Σfiui
N
 × h = 45 -
6
150
 × 10 = 45 - 0.4 = 44.6
Standard deviation (σ2) =
h
N
√NΣfiui2−(Σfiui)2 =
10
150
√150×366−(−6)2 =
1
15
√54900−36
=
1
15
 × 234.23 = 15.61
The group which have greater S.D. is more variable. Thus group B is more variable.

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