The variance $\sigma^2$ of the data
| $x_i$ | 0 | 1 | 5 | 6 | 10 | 12 | 17 |
|---|---|---|---|---|---|---|---|
| $f_i$ | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
is _________.
Answer (integer)
29
Solution
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<col style="width: 123px">
<col style="width: 99px">
<col style="width: 203px">
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<thead>
<tr>
<th class="tg-baqh">$\mathrm{x_i}$</th>
<th class="tg-baqh">$\mathrm{f_i}$</th>
<th class="tg-baqh">$\mathrm{f_i x_i}$</th>
<th class="tg-baqh">$\mathrm{f_i x^2_i}$</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-baqh">0</td>
<td class="tg-baqh">3</td>
<td class="tg-baqh">0</td>
<td class="tg-baqh">0</td>
</tr>
<tr>
<td class="tg-baqh">1</td>
<td class="tg-baqh">2</td>
<td class="tg-baqh">2</td>
<td class="tg-baqh">2</td>
</tr>
<tr>
<td class="tg-baqh">5</td>
<td class="tg-baqh">3</td>
<td class="tg-baqh">15</td>
<td class="tg-baqh">75</td>
</tr>
<tr>
<td class="tg-baqh">6</td>
<td class="tg-baqh">2</td>
<td class="tg-baqh">12</td>
<td class="tg-baqh">72</td>
</tr>
<tr>
<td class="tg-baqh">10</td>
<td class="tg-baqh">6</td>
<td class="tg-baqh">60</td>
<td class="tg-baqh">600</td>
</tr>
<tr>
<td class="tg-baqh">12</td>
<td class="tg-baqh">3</td>
<td class="tg-baqh">36</td>
<td class="tg-baqh">432</td>
</tr>
<tr>
<td class="tg-baqh">17</td>
<td class="tg-baqh">3</td>
<td class="tg-baqh">51</td>
<td class="tg-baqh">867</td>
</tr>
<tr>
<td class="tg-baqh"></td>
<td class="tg-baqh">$\Sigma \mathrm{f}_{\mathrm{i}}=22$</td>
<td class="tg-baqh"></td>
<td class="tg-baqh">$\Sigma \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2=2048$</td>
</tr>
</tbody>
</table></p>
<p>$$\begin{aligned}
& \therefore \quad \Sigma \mathrm{f}_{\mathrm{i}} \mathrm{X}_{\mathrm{i}}=176 \\
& \text { So } \overline{\mathrm{x}}=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}=\frac{176}{22}=8 \\
& \text { for } \sigma^2=\frac{1}{\mathrm{~N}} \sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}{ }^2-(\overline{\mathrm{x}})^2 \\
& =\frac{1}{22} \times 2048-(8)^2 \\
& =93.090964 \\
& =29.0909 \\
&
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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