<div class="main">
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Blue-punch-card-front-horiz.png/320px-Blue-punch-card-front-horiz.png" class="right">
<p>You start to get the hang of using the punch card system. It was invented by Herman Hollerith in the late 19th century to speed up massive counting operations like, specifically, the the US Census. Hollerith's company eventually became part of International Business Machines (IBM). IBM provides the machines used by the Columbia Statistical Bureau.</p>
[[next]]
</div><div class="main">
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Cherokee_syllabary_original_order.png/640px-Cherokee_syllabary_original_order.png" class="left" width="480">
<p>Mary Ross explains a new task for you. "I need you to learn the Cherokee syllabary," she says and hands you a chart. "Once you have a basic familiarity with it, you can start going through these books and article printed in Cherokee and enter the word count, in syllables, and frequency of each syllable."
<br>You look at the clock but get right to work.</p>
[[next|third]]
</div><div class="main">
<table>
<tr><th colspan="10"></tr>
<tr><td>syllabics</td>
<td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr>
<tr><td>frequency</td>
<td>12</td><td>17</td><td>11</td><td>10</td><td>8</td><td>6</td><td>5</td><td>1</td></tr>
</table>
<p>You manage to recognize the syllabics enough to start counting them in a short excerpt. Mary Ross looks at your table and asks you to quickly give the median syllable length.</p>
[[next|fourth]]
</div>
(set: $combo to (num:(prompt: "Enter the median:", "")))
(if: $combo is 4)[(go-to:"correct")]
(else:)[(go-to:"wrong")]correct<div class="main">
<table>
<tr><th colspan="10"></tr>
<tr><td>syllablics</td>
<td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr>
<tr><td>frequency</td>
<td>12</td><td>17</td><td>11</td><td>10</td><td>8</td><td>6</td><td>5</td><td>1</td></tr>
</table>
<p>Mary Ross then asks you to calculate the **mean** syllable length (rounded to the tenth).</p>
[[next|fifth]]
</div><div class="main">
<img src="https://upload.wikimedia.org/wikipedia/en/1/1c/Photo_of_Mary_Golda_Ross.jpg" class="right">
<p>Mary Ross suggests that you look again and think about how many total syllables you counted and so where would the halfway point be.</p>
[[next|third]](set: $combo to (num:(prompt: "Enter the mean:", "")))
(if: $combo is 4.4)[(go-to:"right")]
(else:)[(go-to:"incorrect")]<div class="main">
<img src="https://commons.trincoll.edu/hartfordbrain/files/2021/11/images.jpeg" class="left">
<p>Looking at the data more, you get into a discussion with Ross about the Cherokee language. Someone joins the discussion and Ross introduces him. "This is Benjamin Whorf."<br>You ask if he is part of the linguistics or anthropology department at Columbia University. "No," he replies. "I'm actually here for my work in fire insurance data. Studying American Indian languages is something I do on my own."
<br>You wonder how many insurance inspectors would try to learn any indigenous language.</p>
[[next|sixth]]
</div><div class="main">
<img src="https://upload.wikimedia.org/wikipedia/en/1/1c/Photo_of_Mary_Golda_Ross.jpg" class="right">
<p>Mary Ross suggests that you look again and think about how you need to weight the syllables by the frequency. It's as if you were finding the mean by adding 12 twos and 17 threes and so on, before dividing by 70 (the total number of syllabics).</p>
[[next|correct]]<div class="main">
<p>Whorf explains that insurance companies try to learn about variations in fire losses so that they can set reasonable premiums. Finding the average fire losses isn't enough if there's years of very high losses against low losses. The insurance company needs to estimate what they should set aside as reserves for years of high losses.
<br>You think you follow but ask for a simple example.</p>
[[next|seventh]]
</div><div class="main">
<p>"Suppose we look at a six-sided die," Whorf says. "The mean is 3.5, easy enough." You think about the symmetry and also quickly do (1+2+3+4+5+6)/6 and agree.<br><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Glow_In_The_Dark_D20_Dice.jpg/320px-Glow_In_The_Dark_D20_Dice.jpg" class="right" width="240">
"The standard deviation is a little bit harder to calculate but it's right around 1.71. Now let's look at this 20-sided die," he continues, pulling a strange die out of his pocket. "The mean here is 10.5 and the standard deviation is about 5.77." You don't even try to calculate that standard deviation, but it seems right.<br>
"If we roll three of the six-sided dice, we get a mean of 10.5 as well. But do you think the standard deviation will be also 5.77?" You're not sure, but the way he said it makes you think not.</p>
[[next|eighth]]<div class="main">
<p>"The standard deviation for the sum of three six-sided dice is only 2.96. We get that by adding the variances, that is the square of the standard deviation, and then taking the square root. So the square root of 1.71 squared times 3." You think you follow. "This mean we can have the same average when rolling a 20-sided die and 3 six-sided dice but a lot more variability with the 20-sided die. Insurance companies try to model the 'nice' situation of many independent losses, the 3 six-sided dice, versus the 'not-so-nice' situation of a few dependent losses, the 20-sided die. Maybe fire losses aren't independent of each other and there could be a year with really high losses."</p>
[[next|ninth]]
</div><div class="main">
<img src="https://cdn4.picryl.com/photo/2019/09/14/national-atlas-indian-tribes-cultures-and-languages-united-states-81e062-1024.jpg" class="left" width="500">
{(set: $code to (random: 50, 350) * 37 + 2)}
<p>Mary Ross gets you started inputting the data provided by Whorf onto punch cards. While you work carefully, you still thinking in the back of your mind about American Indian languages and how to study them with statistics.</p>
<p>//your completion code: $code//</p>
</div>