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<p>A climate research organization has a time-series dataframe with daily temperature readings for different cities. This dataframe has three columns: <strong><code>date</code></strong>, <strong><code>city</code></strong>, and <strong><code>temperature</code></strong>.</p>

<p>Due to data recording issues, the temperature reading for some days might be missing. The organization requires the temperature readings for each day, so they ask you to interpolate the missing data.</p>

<p>Write a Python function using Pandas that uses a <strong>linear interpolation</strong> to estimate the missing data and fill out the dataframe.</p>

<p><strong><em>Notes:</em></strong></p>

<ul>
<li><em>When estimating the missing values for a city, the interpolation should only consider data from the same city.</em></li>
<li><em>Temperature recording issues are rare, so you can assume that there is no missing data two days in a row.</em></li>
<li><em>You can also assume that both the first and the last dates in your dataframe hold valid temperature data.</em></li>
</ul>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<table>
<thead>
<tr>
<th align="center">date</th>
<th align="center">city</th>
<th align="center">temperature</th>
</tr>
</thead>

<tbody>
<tr>
<td align="center">2023-01-01</td>
<td align="center">London</td>
<td align="center">10</td>
</tr>

<tr>
<td align="center">2023-01-02</td>
<td align="center">London</td>
<td align="center">NaN</td>
</tr>

<tr>
<td align="center">2023-01-03</td>
<td align="center">London</td>
<td align="center">12</td>
</tr>

<tr>
<td align="center">2023-01-04</td>
<td align="center">London</td>
<td align="center">NaN</td>
</tr>

<tr>
<td align="center">2023-01-05</td>
<td align="center">London</td>
<td align="center">14</td>
</tr>

<tr>
<td align="center">2023-01-01</td>
<td align="center">Berlin</td>
<td align="center">-2</td>
</tr>

<tr>
<td align="center">2023-01-02</td>
<td align="center">Berlin</td>
<td align="center">-1</td>
</tr>

<tr>
<td align="center">2023-01-03</td>
<td align="center">Berlin</td>
<td align="center">NaN</td>
</tr>

<tr>
<td align="center">2023-01-04</td>
<td align="center">Berlin</td>
<td align="center">1</td>
</tr>

<tr>
<td align="center">2023-01-05</td>
<td align="center">Berlin</td>
<td align="center">2</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th align="center">date</th>
<th align="center">city</th>
<th align="center">temperature</th>
</tr>
</thead>

<tbody>
<tr>
<td align="center">2023-01-01</td>
<td align="center">London</td>
<td align="center">10</td>
</tr>

<tr>
<td align="center">2023-01-02</td>
<td align="center">London</td>
<td align="center">11</td>
</tr>

<tr>
<td align="center">2023-01-03</td>
<td align="center">London</td>
<td align="center">12</td>
</tr>

<tr>
<td align="center">2023-01-04</td>
<td align="center">London</td>
<td align="center">13</td>
</tr>

<tr>
<td align="center">2023-01-05</td>
<td align="center">London</td>
<td align="center">14</td>
</tr>

<tr>
<td align="center">2023-01-01</td>
<td align="center">Berlin</td>
<td align="center">-2</td>
</tr>

<tr>
<td align="center">2023-01-02</td>
<td align="center">Berlin</td>
<td align="center">-1</td>
</tr>

<tr>
<td align="center">2023-01-03</td>
<td align="center">Berlin</td>
<td align="center">0</td>
</tr>

<tr>
<td align="center">2023-01-04</td>
<td align="center">Berlin</td>
<td align="center">1</td>
</tr>

<tr>
<td align="center">2023-01-05</td>
<td align="center">Berlin</td>
<td align="center">2</td>
</tr>
</tbody>
</table>


Interpolating Missing Temperatures

<p>Let’s say we have a table with an <code>id</code> and <code>name</code> fields. The table holds over 100 million rows and we want to sample a random row in the table without throttling the database.</p>

<p>Write a query to randomly sample a row from this table.</p>

<p><strong>Input:</strong></p>

<p><code>big_table</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>


Write a query to randomly sample a row from a big table.

Random SQL Sample

<p>Let’s say that your company is running a standard control and variant AB test on a feature to increase conversion rates on the landing page. The PM checks the results and finds a .04 p-value.</p>

<p>How would you assess the validity of the result?</p>


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