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<!DOCTYPE html>
<html data-require="math stat math-format word-problems spin">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Reading stem and leaf plots</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="STEMS">randRange( 5, 7 )</var>
<var id="SAMPLES">randRange( 10, 20 )</var>
<var id="TGT_MEAN">randRange( 20, STEMS * 10 - 20 )</var>
<var id="TGT_STDDEV">randRange( 10, 15 )</var>
<var id="RAW_DATA">sortNumbers( $.map( _.range( SAMPLES ), function() {
var dataPoint;
while ( 1 ) {
dataPoint = round( randGaussian() * TGT_STDDEV + TGT_MEAN );
if ( dataPoint &gt;= 0 &amp;&amp; dataPoint &lt; STEMS * 10 ) {
return dataPoint;
}
}
}) )</var>
<var id="DATA">$.map( _.range( STEMS ), function( stem ) {
return [ $.map( RAW_DATA, function( leaf ) {
if ( stem * 10 &lt;= leaf &amp;&amp; leaf &lt; ( stem + 1 ) * 10 ) {
return leaf - ( stem * 10 );
}
}) ];
})</var>
<var id="LOCATION,LOCATION_DISPLAY">randFromArray([
["grocery store", new Plural(function(num) {
return $.ngettext("grocery store", "grocery stores", num);
})],
["department store", new Plural(function(num) {
return $.ngettext("department store", "department stores", num);
})],
["zoo", new Plural(function(num) {
return $.ngettext("zoo", "zoos", num);
})]
])</var>
<var id="ITEM">
{
"grocery store": fruit(1),
"department store": clothing(1),
"zoo": animal(1)
}[ LOCATION ]
</var>
</div>
<div class="problem">
<p class="spin" data-if="LOCATION === 'grocery store'">
{The buyer for|A statistician for|An executive of} a chain of supermarkets created the following stem-and-leaf plot
showing the number of <var>plural_form(ITEM)</var> at each of the stores:
</p>
<p class="spin" data-if="LOCATION === 'department store'">
{The buyer for|A statistician for|The regional manager of} a chain of department stores created the following stem-and-leaf plot
showing the number of <var>plural_form(ITEM)</var> at each of the stores:
</p>
<p class="spin" data-if="LOCATION === 'zoo'">
{The government|A conservation group|A zookeeper} {created|published} the following stem-and-leaf plot
showing the number of <var>plural_form(ITEM)</var> at each major zoo in the country:
</p>
<p>
<code>
\left| \quad \begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
<var>STEM</var>
\vphantom{\Large{0}} \\
</span>
\end{matrix} \quad \right|
\quad
\begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
<span data-each="DATA[ STEM ] as LEAF" data-unwrap=""><var>LEAF</var>&amp;</span>
\vphantom{\Large{0}} \\
</span>
\end{matrix}
</code>
</p>
</div>
<div class="hints">
<p>
The left column of the stem and leaf plot represents the tens place; each number on the right side
represents the ones place for the number of <var>plural_form(ITEM)</var> at a <var>LOCATION_DISPLAY</var>.
</p>
<div>
<p>
We can combine the tens and ones places and write out the number of <var>plural_form(ITEM)</var> at each <var>LOCATION_DISPLAY</var> on the right:
</p>
<p>
<code>
\small{
\left| \space \begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
\color{<var>GREEN</var>}{<var>STEM</var>}
\vphantom{\Large{0}} \\
</span>
\end{matrix} \space \right|
\space
\begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
<span data-each="DATA[ STEM ] as LEAF" data-unwrap="">\color{<var>BLUE</var>}{<var>LEAF</var>}&amp;</span>
\vphantom{\Large{0}} \\
</span>
\end{matrix}
\space
\begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
\rightarrow
\vphantom{\Large{0}} \\
</span>
\end{matrix}
\space
\begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
<span data-each="DATA[ STEM ] as LEAF" data-unwrap="">\color{<var>GREEN</var>}{<var>STEM</var>}\color{<var>BLUE</var>}{<var>LEAF</var>}&amp;</span>
\vphantom{\Large{0}} \\
</span>
\end{matrix}
}
</code>
</p>
</div>
<div>
<p>Now we know the number of <var>plural_form(ITEM)</var> at the different <var>plural_form(LOCATION_DISPLAY)</var>:</p>
<p><code>\qquad</code><var>toSentenceTex( RAW_DATA )</var></p>
</div>
<div>
<p>
<span data-if="TYPE === 'smallest'">What was the fewest number of <var>plural_form(ITEM)</var> at any one <var>LOCATION_DISPLAY</var>?</span>
<span data-else-if="TYPE === 'largest'">What was the largest number of <var>plural_form(ITEM)</var> at any one <var>LOCATION_DISPLAY</var>?</span>
<span data-else="">
<span data-if="TYPE === 'how-many'">
<span data-if="isSingular(AMOUNT)" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have exactly
<var>AMOUNT</var> <var>ITEM</var>?
</span>
<span data-else="" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have exactly
<var>AMOUNT</var> <var>plural_form(ITEM, AMOUNT)</var>?
</span>
</span>
<span data-if="TYPE === 'less-than'">
<span data-if="isSingular(AMOUNT)" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have fewer than
<var>AMOUNT</var> <var>ITEM</var>?
</span>
<span data-else="" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have fewer than
<var>AMOUNT</var> <var>plural_form(ITEM, AMOUNT)</var>?
</span>
</span>
<span data-if="TYPE === 'greater-than'">
<span data-if="isSingular(AMOUNT)" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have more than
<var>AMOUNT</var> <var>ITEM</var>?
</span>
<span data-else="" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have more than
<var>AMOUNT</var> <var>plural_form(ITEM, AMOUNT)</var>?
</span>
</span>
</span>
</p>
<p data-if="SOLUTION > 0">
<code>\qquad</code><var>toSentenceTex( RAW_DATA, IS_SOLUTION, "hint_pink" )</var>
</p>
</div>
<div>
<p>
<code>
\qquad
\left| \quad \begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
<var>STEM</var>
\vphantom{\Large{0}} \\
</span>
\end{matrix} \quad \right|
\quad
\begin{matrix}
<span data-each="STEMS times as STEM" data-unwrap="">
<span data-each="DATA[ STEM ] as LEAF" data-unwrap="">
<span data-if="IS_SOLUTION( STEM * 10 + LEAF )" data-unwrap="">
\color{<var>PINK</var>}{<var>LEAF</var>}&amp;
</span>
<span data-else="" data-unwrap="">
<var>LEAF</var>&amp;
</span>
</span>
\vphantom{\Large{0}} \\
</span>
\end{matrix}
</code>
</p>
<p><strong>
<span data-if="TYPE === 'smallest'">
<span data-if="isSingular(SOLUTION)">
The <var>LOCATION_DISPLAY</var> with the fewest <var>plural_form(ITEM)</var> had <var>SOLUTION</var> <var>ITEM</var>.
</span>
<span data-else="">
The <var>LOCATION_DISPLAY</var> with the fewest <var>plural_form(ITEM)</var> had <var>SOLUTION</var> <var>plural_form(ITEM, SOLUTION)</var>.
</span>
</span>
<span data-else-if="TYPE === 'largest'">
<span data-if="isSingular(SOLUTION)">
The <var>LOCATION_DISPLAY</var> with the most <var>plural_form(ITEM)</var> had <var>SOLUTION</var> <var>ITEM</var>.
</span>
<span data-else="">
The <var>LOCATION_DISPLAY</var> with the most <var>plural_form(ITEM)</var> had <var>SOLUTION</var> <var>plural_form(ITEM, SOLUTION)</var>.
</span>
</span>
<span data-else="">
<span data-if="isSingular(SOLUTION)">
There are <var>SOLUTION</var> <var>LOCATION_DISPLAY</var> that match our question.
</span>
<span data-else="">
There are <var>SOLUTION</var> <var>plural_form(LOCATION_DISPLAY, SOLUTION)</var> that match our question.
</span>
</span>
</strong></p>
</div>
</div>
<div class="problems">
<div id="how-many">
<div class="vars">
<var id="TYPE">"how-many"</var>
<var id="AMOUNT" data-ensure="0 &lt;= AMOUNT &amp;&amp; AMOUNT &lt; STEMS * 10">
random() &lt; 0.7 ?
randFromArray( RAW_DATA ) :
round( randGaussian() * TGT_STDDEV + TGT_MEAN )
</var>
<var id="IS_SOLUTION">function( x ) { return x === AMOUNT; }</var>
<var id="SOLUTION">_.reduce( RAW_DATA, function( memo, num ) { return num === AMOUNT ? ++memo : memo; }, 0 )</var>
</div>
<p class="question">
<span data-if="isSingular(AMOUNT)" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have exactly <var>AMOUNT</var> <var>ITEM</var>?
</span><span data-else="" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have exactly <var>AMOUNT</var> <var>plural_form(ITEM, AMOUNT)</var>?
</span>
</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer" style="padding-right: 5px"><var>SOLUTION</var></span> <var>plural_form(LOCATION_DISPLAY)</var></p>
</div>
</div>
<div id="less-than">
<div class="vars">
<var id="TYPE">"less-than"</var>
<var id="AMOUNT">randRange( 10, (STEMS - 1) * 10 )</var>
<var id="IS_SOLUTION">function( x ) { return x &lt; AMOUNT; }</var>
<var id="SOLUTION">_.reduce( RAW_DATA, function( memo, num ) { return num &lt; AMOUNT ? ++memo : memo; }, 0 )</var>
</div>
<p class="question">
<span data-if="isSingular(AMOUNT)">
How many <var>plural_form(LOCATION_DISPLAY)</var> have fewer than <var>AMOUNT</var> <var>ITEM</var>?
</span><span data-else="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have fewer than <var>AMOUNT</var> <var>plural_form(ITEM, AMOUNT)</var>?
</span>
</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer" style="padding-right: 5px"><var>SOLUTION</var></span> <var>plural_form(LOCATION_DISPLAY)</var></p>
</div>
</div>
<div id="greater-than">
<div class="vars">
<var id="TYPE">"greater-than"</var>
<var id="AMOUNT">randRange( 10, (STEMS - 1) * 10 )</var>
<var id="IS_SOLUTION">function( x ) { return x &gt; AMOUNT; }</var>
<var id="SOLUTION">_.reduce( RAW_DATA, function( memo, num ) { return num &gt; AMOUNT ? ++memo : memo; }, 0 )</var>
</div>
<p class="question">
<span data-if="isSingular(AMOUNT)" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have more than <var>AMOUNT</var> <var>ITEM</var>?
</span><span data-else="" data-unwrap="">
How many <var>plural_form(LOCATION_DISPLAY)</var> have more than <var>AMOUNT</var> <var>plural_form(ITEM, AMOUNT)</var>?
</span>
</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer" style="padding-right: 5px"><var>SOLUTION</var></span> <var>plural_form(LOCATION_DISPLAY)</var></p>
</div>
</div>
<div id="extreme">
<div class="vars">
<var id="TYPE">randFromArray([ "smallest", "largest" ])</var>
<var id="AMOUNT">TYPE === "smallest" ? RAW_DATA[ 0 ] : RAW_DATA[ RAW_DATA.length - 1 ]</var>
<var id="IS_SOLUTION">function( x ) { return x === AMOUNT; }</var>
<var id="SOLUTION">AMOUNT</var>
</div>
<p class="question">
<span data-if="TYPE === 'smallest'">What was the smallest number of <var>plural_form(ITEM)</var> at any one <var>LOCATION_DISPLAY</var>?</span>
<span data-if="TYPE === 'largest'">What was the largest number of <var>plural_form(ITEM)</var> at any one <var>LOCATION_DISPLAY</var>?</span>
</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer" style="padding-right: 5px"><var>SOLUTION</var></span> <var>plural_form(ITEM)</var></p>
</div>
</div>
</div>
</div>
</body>
</html>
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