Mean Median Mode & Range

<p>These four measures help you summarise a set of data with just one or two numbers. The 11+ exam expects you to calculate each one and to understand when each is most useful.</p>

<h2>The Mean (Average)</h2>

<p>Add up all the values and divide by how many values there are.</p>

<p><strong>Worked Example:</strong> Test scores: 7, 5, 8, 6, 9. Mean = (7 + 5 + 8 + 6 + 9) ÷ 5 = 35 ÷ 5 = 7.</p>

<p>The mean does not have to be a whole number. If the total were 36, the mean would be 36 ÷ 5 = 7.2.</p>

<h2>The Median</h2>

<p>The median is the middle value when the data is written in order from smallest to largest.</p>

<p><strong>Worked Example:</strong> Data: 12, 5, 9, 3, 7. First, put in order: 3, 5, 7, 9, 12. The middle value (third out of five) is 7. Median = 7.</p>

<p><strong>Even number of values:</strong> If there is an even number of values, there are two middle values. The median is the mean of these two.</p>

<p><strong>Worked Example:</strong> Data in order: 4, 6, 8, 11. The two middle values are 6 and 8. Median = (6 + 8) ÷ 2 = 7.</p>

<h2>The Mode</h2>

<p>The mode is the value that appears most often. A set of data can have one mode, more than one mode, or no mode at all (if every value appears the same number of times).</p>

<p><strong>Worked Example:</strong> Data: 3, 5, 5, 7, 8, 5, 9. The value 5 appears three times, more than any other. Mode = 5.</p>

<p><strong>Worked Example:</strong> Data: 2, 4, 4, 6, 6, 8. Both 4 and 6 appear twice. This set has two modes (it is "bimodal").</p>

<h2>The Range</h2>

<p>The range measures how spread out the data is. Range = highest value − lowest value.</p>

<p><strong>Worked Example:</strong> Data: 3, 7, 2, 11, 5. Range = 11 − 2 = 9.</p>

<p>The range is not an average — it tells you about the spread, not the centre.</p>

<h2>Using Averages to Solve Problems</h2>

<p><strong>Worked Example:</strong> The mean of 4 numbers is 8. What is their total?</p>

<p>Total = mean × number of values = 8 × 4 = 32. This trick is very useful — if you know the mean and how many values there are, you can find the total.</p>

<p><strong>Worked Example:</strong> The mean of five numbers is 6. Four of the numbers are 4, 7, 5, and 9. What is the fifth number?</p>

<p>Total = 6 × 5 = 30. Sum of four known numbers = 4 + 7 + 5 + 9 = 25. Fifth number = 30 − 25 = 5.</p>

<h2>Which Average to Use?</h2>

<ul>

<li><strong>Mean:</strong> uses all the data, but can be affected by very high or very low values (outliers)</li>

<li><strong>Median:</strong> not affected by outliers, good for skewed data</li>

<li><strong>Mode:</strong> useful for categories (like favourite colour), where you cannot calculate a mean</li>

</ul>

<h2>Practice Tips</h2>

<ul>

<li>For the median, always put the data in order FIRST — a very common mistake is to skip this step</li>

<li>The mean does not have to be one of the values in the data set</li>

<li>Remember: mean = total ÷ count, so total = mean × count</li>

<li>Check your mean by estimating: if most values are around 7, a mean of 35 is clearly wrong</li>

<li>The range is a single number, not a pair of numbers — just subtract</li>

</ul>