<p style="text-align:justify"><span style="font-size:14px"><strong><span style="color:black">Variation</span></strong><span style="color:black">&nbsp;is present in any set of data. For example, 16-ml cans of beverage may contain more or less than 16 ml of liquid. In one study, eight 16 ml cans were measured and produced the following amount (in ml) of beverage:</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p><span style="font-size:14px"><span style="color:black">15.8;&nbsp;16.1;&nbsp;15.2;&nbsp;14.8;&nbsp;15.8;&nbsp;15.9;&nbsp;16.0;&nbsp;</span></span></p>

<p><span style="font-size:14px"><span style="color:black">15.5</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Measurements of the amount of beverage in a 16-ml can may vary because different people make the measurements or because the exact amount, 16 ml of liquid, was not put into the cans. Manufacturers regularly run tests to determine if the amount of beverage in a 16-ml can falls within the desired range.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Be aware that as you take data, your data may vary somewhat from the data someone else is taking for the same purpose. This is completely natural. However, if two or more of you are taking the same data and get very different results, it is time for you and the others to reevaluate your data-taking methods and your accuracy</span><span style="color:#424242">.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p><span style="font-size:14px"><span style="color:#000000"><strong>Variation in Samples</strong></span></span></p>

<p>&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">It was mentioned previously that two or more&nbsp;<strong>samples</strong>&nbsp;from the same&nbsp;<strong>population</strong>, taken randomly, and having close to the same characteristics of the population will likely be different from each other. Suppose <u><span style="color:teal">Dhruv </span></u>and Jeet both decide to study the average amount of time students at their college sleep each night. <u><span style="color:teal">Dhruv</span></u> and Jeet each take samples of 500 students. Doreen uses systematic sampling and Jeet uses cluster sampling. <u><span style="color:teal">Dhruv </span></u>&#39;s sample will be different from Jeet&#39;s sample. Even if <u><span style="color:teal">Dhruv</span></u> and Jeet used the same sampling method, in all likelihood their samples would be different. Neither would be wrong, however.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Think about what contributes to making Dhruv&rsquo;s and Jeet&rsquo;s samples different.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">If Dhruv<u><span style="color:teal"> </span></u>and Jeet took larger samples (i.e. the number of data values is increased), their sample results (the average amount of time a student sleeps) might be closer to the actual population average. But still, their samples would be, in all likelihood, different from each other. This&nbsp;<strong>variability in samples</strong>&nbsp;cannot be stressed enough.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p><span style="font-size:14px"><strong><span style="color:#2e74b5"><span style="color:black">Size of a Sample</span></span></strong></span></p>

<p>&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The size of a sample (often called the number of observations, usually given the symbol n) is important. The examples you have seen in this book so far have been small. Samples of only a few hundred observations, or even smaller, are sufficient for many purposes. In polling, samples that are from 1,200 to 1,500 observations are considered large enough and good enough if the survey is random and is well done. Later we will find that even much smaller sample sizes will give very good results. You will learn why when you study confidence intervals.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p><span style="font-size:14px"><span style="color:black">Be aware that many large samples are biased. For example, call-in surveys are invariably biased, because people choose to respond or not.</span></span></p>