Average:. An average is set of numbers, you add all the items and divided the total by the number of items. While to calculate a percentage,  multiply the fractions by 100(%).

<h2>Mathematical Skills in Biology</h2>
<p>Mathematical skills are important in Biology. Below are explanations of some of the skills you will encounter.</p>
<p><em class="emphasis">NB.</em> You must state the UNITS at the end of each calculation, e.g. cm, degrees, kg, etc.</p>
<h3>Scales</h3>
<p>A scale is given in a diagram, drawing or <a data-lesson="electron-orbitals" data-subject="biology" data-tutorial="chemical-foundation-of-life" href="https://app.ulearngo.com/biology/chemical-foundation-of-life/electron-orbitals">electron</a> micrograph so that the actual size of the object that is being shown can be determined. The object could be bigger or smaller in real life.</p>
<p>Example: To measure the diameter of a <a data-lesson="chloroplast" data-subject="biology" data-tutorial="cell-biology" href="https://app.ulearngo.com/biology/cell-biology/chloroplast">chloroplast</a> with a scale line of 1 µm.</p>
<p>1) Measure the length of the scale line on the micrograph in mm, e.g. 1 µm = 17mm</p>
<p>2) Measure the diameter of the organelle in millimetres, e.g. = 60mm</p>
<p>3) True diameter of chloroplast:</p>
<h4>\(= \cfrac{\text{measured size} × \text{true length of scale line}}{\text{measured length of scale line}}\)</h4>
<h4>\(= \cfrac{60\text{ mm} × 1\text{ μm}}{17\text{ mm}}\)</h4>
<h4>\(= 3.53\text{ μm}\)</h4>
<h3>Averages</h3>
<p>To find an average of a set of numbers, you add all the items and divide the total by the number of items.</p>
<p>Example: Find the average height in a class of 10 learners with the following heights in cm: 173, 135, 142, 167, 189, 140, 139, 164, 172, 181 cm.</p>
<p>Total = 1602 (add all 10 heights together)</p>
<h4>\(\text{Average} = \cfrac{1602}{10}\)</h4>
<h4>\(= 160.2\text{ cm}\)</h4>
<h3><b class="emphasis">Percentages</b></h3>
<p>To calculate a percentage, multiply the fraction by 100.</p>
<p>Formula for calculating percentage (%):</p>
<h4>\(\text{Percentage} = \cfrac{\text{Number with feature }(A)}{\text{Total number }(B)} × 100\)</h4>
<p><strong>Example:</strong> Calculate the percentage of learners in your class that are left-handed.</p>
<p>1) Count how many learners are left handed (A).</p>
<p>2) Count the total number of learners in the class (B).</p>
<p>There are 48 learners and 4 of them are left handed.</p>
<p>Therefore, % of left-handed:</p>
<h4>\(= \cfrac{A}{B} × 100\)</h4>
<h4>\(= \cfrac{4}{48} × 100\)</h4>
<h4>\(= 8.3\%\)</h4>
<p>8.3% of the learners in your class are left-handed.</p>
<p>The percentage of right-handed learners:</p>
<h4>\(= 100 \; - \; 8.3\)</h4>
<h4>\(= 91.7\%\)</h4>
<p>91.7% of the learners in your class are right-handed.</p>
<h3><b class="emphasis">Some Conversions</b></h3>
<table>
<tbody>
<tr>
<td><b class="emphasis">From unit:</b></td>
<td colspan="4"><b class="emphasis">To unit (number of these units per “From unit”):</b></td>
</tr>
<tr>
<td> </td>
<td><b class="emphasis">m</b></td>
<td><b class="emphasis">mm</b></td>
<td><b class="emphasis">µm</b></td>
<td><b class="emphasis">nm</b></td>
</tr>
<tr>
<td>m</td>
<td>1</td>
<td>1000</td>
<td>1 000 000</td>
<td>1 000 000 000</td>
</tr>
<tr>
<td>mm</td>
<td>10<sup class="sup">−3</sup> or 1/1000</td>
<td>1</td>
<td>1000</td>
<td>1 000 000</td>
</tr>
<tr>
<td>µm (micrometres)</td>
<td>10<sup class="sup">−6</sup> or 1/1 000 000</td>
<td>10<sup class="sup">−3</sup> or 1/1000</td>
<td>1</td>
<td>1000</td>
</tr>
<tr>
<td>nm (nanometres)</td>
<td>10<sup class="sup">−9</sup> or 1/1 000 000 000</td>
<td>10<sup class="sup">−6</sup> or 1/1 000 000</td>
<td>10<sup class="sup">−3</sup> or 1/1000</td>
<td>1</td>
</tr>
</tbody>
</table>

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Mathematical Skills in Biology

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Mathematical Skills in Biology

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