Python Mean Median Mode

Last modified on: October 20, 2024

<h2>Mean Median Mode - A Statistical Overview</h2>
<p>Explore the concepts of mean, median, and mode in statistics. Learn how to calculate each measure and understand their significance in data analysis with Python examples.</p>
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<h3>Understanding Mean, Median, and Mode</h3>
<p>Mean, median, and mode are fundamental concepts in statistics that help summarize and describe data distributions. Here&rsquo;s a breakdown of each measure, along with examples and Python code to compute them.</p>
<h4>1. <strong>Mean</strong></h4>
<p>The mean, often referred to as the average, is calculated by summing all the numbers in a dataset and dividing by the count of those numbers.</p>
<p><strong>Formula</strong>:<br /><span class="katex"><span class="katex-mathml">Mean=&sum;i=1nxin\text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord text"><span class="mord">Mean</span></span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight">&sum;</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span>1</span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">n</span></span><span class="vlist-s"></span></span></span><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s"></span></span></span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span></p>
<p><strong>Example</strong>:</p>
<ul>
<li>Dataset: [10, 20, 30, 40, 50]</li>
<li>Calculation: <span class="katex-display"><span class="katex"><span class="katex-mathml">Mean=10+20+30+40+505=1505=30\text{Mean} = \frac{10 + 20 + 30 + 40 + 50}{5} = \frac{150}{5} = 30</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord text"><span class="mord">Mean</span></span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">510<span class="mbin">+</span>20<span class="mbin">+</span>30<span class="mbin">+</span>40<span class="mbin">+</span>50</span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">5150</span><span class="vlist-s"></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">30</span></span></span></span></span></li>
</ul>
<p><strong>Python Code</strong>:</p>
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<pre class="language-python"><code>data = [10, 20, 30, 40, 50]
mean = sum(data) / len(data)
print("Mean:", mean)</code></pre>
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<h4>2. <strong>Median</strong></h4>
<p>The median is the middle value in a dataset when the numbers are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.</p>
<p><strong>Example</strong>:</p>
<ul>
<li>Odd number of elements: Dataset: [10, 20, 30, 40, 50] &rarr; Median is 30.</li>
<li>Even number of elements: Dataset: [10, 20, 30, 40] &rarr; Median is <span class="katex"><span class="katex-mathml">(20+30)/2=25(20 + 30) / 2 = 25</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mopen">(</span><span class="mord">20</span><span class="mbin">+</span></span><span class="base"><span class="mord">30</span><span class="mclose">)</span><span class="mord">/2</span><span class="mrel">=</span></span><span class="base"><span class="mord">25</span></span></span></span>.</li>
</ul>
<p><strong>Python Code</strong>:</p>
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<pre class="language-python"><code>data = [10, 20, 30, 40, 50]
sorted_data = sorted(data)
n = len(sorted_data)

if n % 2 == 0:
    median = (sorted_data[n//2 - 1] + sorted_data[n//2]) / 2
else:
    median = sorted_data[n//2]

print("Median:", median)</code></pre>
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<h4>3. <strong>Mode</strong></h4>
<p>The mode is the value that appears most frequently in a dataset. A dataset may have one mode, more than one mode, or no mode at all.</p>
<p><strong>Example</strong>:</p>
<ul>
<li>Dataset: [10, 20, 20, 30, 40] &rarr; Mode is 20.</li>
<li>Dataset: [10, 20, 30, 40] &rarr; No mode (all values occur once).</li>
<li>Dataset: [10, 10, 20, 20, 30] &rarr; Modes are 10 and 20 (bimodal).</li>
</ul>
<p><strong>Python Code</strong>:</p>
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<pre class="language-python"><code>from collections import Counter

data = [10, 20, 20, 30, 40]
data_count = Counter(data)
mode_data = data_count.most_common()

max_count = mode_data[0][1]
modes = [x[0] for x in mode_data if x[1] == max_count]

print("Mode:", modes)</code></pre>
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<h3>Summary</h3>
<ul>
<li><strong>Mean</strong>: Average of the dataset.</li>
<li><strong>Median</strong>: Middle value of the dataset.</li>
<li><strong>Mode</strong>: Most frequently occurring value(s) in the dataset.</li>
</ul>
<p>These three measures provide a comprehensive view of the central tendency of a dataset, and each is useful in different statistical contexts.</p>
<h3>&nbsp;</h3>
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